#TL;DR The best options for reducing your in-flight waste are to use a budget airline with no in-flight service, or declaring days in advance of your flight that you don't want an in-flight meal on a full-service airline. If waste minimisation is a concern, you should first address the huge CO2 emission cost first, and seriously considering not taking the flight in the first place.

#CO2 First and foremost, the largest environmental concern in taking a flight is the CO2 emissions. Using the link provided by Rsf, a 10 hour flight could produce in the order of 900kg of CO2, a significant chunk of the average yearly carbon footprint of a single person. But for the sake of answering the question, we're only going to look at in-flight waste. Perhaps a large CO2 offset has been purchased to try and mitigate emissions, or perhaps an individual is tracking a CO2 budget and has accounted for the flight. If you are not at least doing this, then waste minimisation will make a comparatively tiny impact on the environmental cost of your flight.

#Waste According to IATA (thanks Zach Lipton for the link) a typical passenger on average creates 1.43kg of waste, of which 40% is food and plastic waste (~0.6kg). This is averaged across all flights, so presumably long haul flights will have more waste, and potentially a larger proportion of that will be food and plastic waste. So where does this waste come from, and what can we do?

#Snacks and miscellaneous For small service items, like drinks, peanuts etc. the simple option is to refuse. Peanuts will keep, and so will the cups, cans, bottles etc. etc. to be passed onto the next person. (To counter the anticipated "but it's going to be used anyway", the overall demand will be reduced, hence the airline won't purchase as much). For other things that might come in plastic, again you can just refuse to use them and leave them as they are. Be aware though that sometimes blankets can be wrapped in plastic, so if you think you'll need one, you might have to wear an extra layer just in case.

#In-flight meals For things like the in-flight meals, it becomes a bit trickier. If you haven't planned ahead, then the moment the tray lands on your table is probably too late to do much about it. In fact, according to Dan, your trays are packed several hours before you even board the flight. What happens to the waste afterwards is in the hands of the contractor, and if you don't use something from your tray, there is a strong likelihood it will be discarded anyway.

#Plan ahead

#What impact will this have? In exact terms, minimising your in-flight waste might impact your own personal environmental cost, but on the scale of the flight you take, the impact will be tiny. But this is true of almost any action a person takes in any sphere. The value of this comes from the message sent to the airlines about what their customers care about. As Harper points out, this is an issue with the entire system and requires ingenuity from a top level. SSight3 suggests documenting good practices you observe and passing them on to other airlines. But there is a lot going on behind the scenes that regular passengers simply won't see. Perhaps the best option is making sure airlines know that in-flight waste is a concern but telling them directly, perhaps through customer complaint channels. Again, the biggest environmental impact you can have is from not taking the flight in the first place.

TL;DR

The best options for reducing your in-flight waste are to use a budget airline with no in-flight service, or declaring days in advance of your flight that you don't want an in-flight meal on a full-service airline. If waste minimisation is a concern, you should first address the huge CO2 emission cost first, and seriously considering not taking the flight in the first place.

CO2

First and foremost, the largest environmental concern in taking a flight is the CO2 emissions. Using the link provided by Rsf, a 10 hour flight could produce in the order of 900kg of CO2, a significant chunk of the average yearly carbon footprint of a single person. But for the sake of answering the question, we're only going to look at in-flight waste. Perhaps a large CO2 offset has been purchased to try and mitigate emissions, or perhaps an individual is tracking a CO2 budget and has accounted for the flight. If you are not at least doing this, then waste minimisation will make a comparatively tiny impact on the environmental cost of your flight.

Waste

According to IATA (thanks Zach Lipton for the link) a typical passenger on average creates 1.43kg of waste, of which 40% is food and plastic waste (~0.6kg). This is averaged across all flights, so presumably long haul flights will have more waste, and potentially a larger proportion of that will be food and plastic waste. So where does this waste come from, and what can we do?

Snacks and miscellaneous

For small service items, like drinks, peanuts etc. the simple option is to refuse. Peanuts will keep, and so will the cups, cans, bottles etc. etc. to be passed onto the next person. (To counter the anticipated "but it's going to be used anyway", the overall demand will be reduced, hence the airline won't purchase as much). For other things that might come in plastic, again you can just refuse to use them and leave them as they are. Be aware though that sometimes blankets can be wrapped in plastic, so if you think you'll need one, you might have to wear an extra layer just in case.

In-flight meals

For things like the in-flight meals, it becomes a bit trickier. If you haven't planned ahead, then the moment the tray lands on your table is probably too late to do much about it. In fact, according to Dan, your trays are packed several hours before you even board the flight. What happens to the waste afterwards is in the hands of the contractor, and if you don't use something from your tray, there is a strong likelihood it will be discarded anyway.

Plan ahead

What impact will this have?

In exact terms, minimising your in-flight waste might impact your own personal environmental cost, but on the scale of the flight you take, the impact will be tiny. But this is true of almost any action a person takes in any sphere. The value of this comes from the message sent to the airlines about what their customers care about. As Harper points out, this is an issue with the entire system and requires ingenuity from a top level. SSight3 suggests documenting good practices you observe and passing them on to other airlines. But there is a lot going on behind the scenes that regular passengers simply won't see. Perhaps the best option is making sure airlines know that in-flight waste is a concern but telling them directly, perhaps through customer complaint channels. Again, the biggest environmental impact you can have is from not taking the flight in the first place.

There are a lot of replies to this question and there are bits of an answer spread all over, but frustratingly the discussion has been dominated by CO2 emissions, rather than addressing the question asked. I'm going to collect the valuable information here and add in some of my own research. Please feel free to improve this answer, it is a community wiki (but you don't need to add any more about CO2, there are already very well thought out answers that do this).

As noted by averell, budget airlines are often forgoing the traditional in-flight service, in favour of a "buy in advance" model (to coin a phrase). Choosing these airlines will allow you to virtually eliminate your waste by eating a sufficient meal before boarding, or preparing a light meal to take on board. If you are flying a full cost airline, then you usually have an option to specify your meal (people with dietary requirements will be well aware of this). In some cases you can request "no meal" and do the same as above.

If you take this route, then weight minimisation is something you should also consider, but you should be accounting for the upper limit of your CO2 emissions in your offset/budget anyway.

There are a lot of replies to this question and there are bits of an answer spread all over, but the discussion has been dominated by CO2 emissions, rather than addressing the question asked. I'm going to collect the valuable information here and add in some of my own research. Please feel free to improve this answer, it is a community wiki (but you don't need to add any more about CO2, there are already very well thought out answers that do this).

#TL;DR The best options for reducing your in-flight waste are to use a budget airline with no in-flight service, or declaring days in advance of your flight that you don't want an in-flight meal on a full-service airline. If waste minimisation is a concern, you should first address the huge CO2 emission cost first, and seriously considering not taking the flight in the first place.

As noted by averell, budget airlines are often forgoing the traditional in-flight service, in favour of a "buy in advance" model (to coin a phrase). Choosing these airlines will allow you to virtually eliminate your in-flight waste by eating a sufficient meal before boarding, or preparing a light meal to take on board. If you are flying a full cost airline, then you usually have an option to specify your meal (people with dietary requirements will be well aware of this). In some cases you can request "no meal" and do the same as above.

If you take this route, then weight minimisation is something you should also consider, but you should be accounting for the upper limit of your CO2 emissions in your offset/budget anyway.

#What impact will this have? In exact terms, minimising your in-flight waste might impact your own personal environmental cost, but on the scale of the flight you take, the impact will be tiny. But this is true of almost any action a person takes in any sphere. The value of this comes from the message sent to the airlines about what their customers care about. As Harper points out, this is an issue with the entire system and requires ingenuity from a top level. SSight3 suggests documenting good practices you observe and passing them on to other airlines. But there is a lot going on behind the scenes that regular passengers simply won't see. Perhaps the best option is making sure airlines know that in-flight waste is a concern but telling them directly, perhaps through customer complaint channels. Again, the biggest environmental impact you can have is from not taking the flight in the first place.

#In-flight meals For things like the in-flight meals, it becomes a bit trickier. If you haven't planned ahead, then the moment the tray lands on your table is probably too late to do much about it. The link provided by Dmitry Grigoryev suggests that in some countries, anything you touch on international flights will be incinerated for biosecurity reasons (although there is a push to temper these laws). However, if you aren't landing in one of these countries, or your flight is domestic, some of your plastic might be reused. To quote this news report from 2010: "Air New Zealand says its plastic utensils, including cutlery, trays, bowls, cups and plates, are sorted by staff for cleaning and reuse following international flights", although it doesn't specify if this is light plastic or not. It also mentions that plastic cutlery on some airlines is actually being sterilised and reused upto 10 times, and potentially as many as 30 times. Using it and returning it to the staff could be a reasonable option if you know the airline does this.

As noted by averell, budget airlines are often forgoing the traditional in-flight service, in favour of a "buy in advance" model (to coin a phrase). Choosing these airlines will allow you to virtually eliminate your waste by eating a sufficient meal before boarding, or preparing a light meal to take on board. If you are flying a full cost airline, then you usually have an option to specify your meal (people with dietary requirements will be well aware of this). In some cases you can request "no meal" and do the same as above.

#In-flight meals For things like the in-flight meals, it becomes a bit trickier. If you haven't planned ahead, then the moment the tray lands on your table is probably too late to do much about it. In fact, according to Dan, your trays are packed several hours before you even board the flight. What happens to the waste afterwards is in the hands of the contractor, and if you don't use something from your tray, there is a strong likelihood it will be discarded anyway.

The link provided by Dmitry Grigoryev suggests that in some countries, anything you touch on international flights will be incinerated for biosecurity reasons (although there is a push to temper these laws). However, if you aren't landing in one of these countries, or your flight is domestic, some of your plastic might be reused. To quote this news report from 2010: "Air New Zealand says its plastic utensils, including cutlery, trays, bowls, cups and plates, are sorted by staff for cleaning and reuse following international flights", although it doesn't specify if this is light plastic or not. It also mentions that plastic cutlery on some airlines is actually being sterilised and reused upto 10 times, and potentially as many as 30 times. Using it and returning it to the staff could be a reasonable option if you know the airline does this.

As noted by averell, budget airlines are often forgoing the traditional in-flight service, in favour of a "buy in advance" model (to coin a phrase). Choosing these airlines will allow you to virtually eliminate your waste by eating a sufficient meal before boarding, or preparing a light meal to take on board. If you are flying a full cost airline, then you usually have an option to specify your meal (people with dietary requirements will be well aware of this). In some cases you can request "no meal" and do the same as above.

If you take this route, then weight minimisation is something you should also consider, but you should be accounting for the upper limit of your CO2 emissions in your offset/budget anyway.