I'm one of those who buys new things before a trip and I even get my dry-cleaning folded which the cleaners put in a plastic bag. Now thinking about it I wonder if it's only a matter of time before I'll be hassled. I was inspired to ask this question by the show "Border Security" where security were even going online to check prices of stuff in people's luggage...so how do prove that in fact everything you own is used and not new? The other thing is some things I buy for a trip I never do use.
For a start, if it's in a box, it's going to look new. So chuck out any packaging.
If it's a camera/cellphone/computer, if you've got stuff on it, that's easy to show it's been used - you can turn it on and show them you actively use it.
For clothing etc, there's not much really, but hopefully all price tags were long removed too. Photos of you in the clothing may help, if the clothing is yours.
In the end - 'how does one not get hassled' - well, we can't control the customs officers, but we can be open, and honest. Declare anything that IS new, which helps alleviate their worries.
In essence, if something else is 'off' - eg your story about your trip, or something you didn't declare but maybe should have, it's going to make them question more about you.
Be prepared, have your documents ready, and don't have anything missing (eg train tickets, accommodation address and so on). Have everything packed well and easily accessible.
Saying that, I've often bought cameras / kindles / laptops before travelling, and never once been asked about how new it is, and that's after 60-something countries. I get other questions far more frequently though.
Depending on your nationality, some countries allow you to declare new items of value before you depart the country, so that when you return there is a record that you had it before you left home. Both the US and Canada have a system for doing this and I imagine many other developed nations do as well.
If you have bought anything of higher value such as camera gear, electronics and such, this would be an advisable thing to look into and use.
For things like new clothes or other everyday items, there is not much you can do except explain to customs that you had them beforehand. The chances of a custom officer harassing you over a nicely pressed shirt is pretty slim (unless of course you have a whole suitcase full).
Most countries allow you a certain amount of duty free and unless you are bringing in lots of stuff you are actually purchasing overseas, even if they did try to ding you for your new shirts, they should be covered under your duty free allowance.
In some countries (like Brazil) you cannot declare an item as you leave. People started using it to obtain a legal receipt to items they managed to smuggle inside the country. Now the only accepted form to prove an item was your prior to your trip is having the original receipt with the date you bought it. As a side note, in Brazil (I don't know how does that work in other countries) personal items such as clothing, 1 cell-phone, 1 non-professional camera, etc. are not subject to importation duties and do not count for the US$500 limit to free importation of foreign items.
Back to your question, the original receipt you get when you buy the item is probably your best choice to proof something was your before you started your trip. All others can be questioned by a bad-mood immigration officer, I think.