If you live in a house and are going away at a time when temperatures get below freezing, you should (many insurance companies insist) have someone stop by the house every few days to make sure the heat is on and the pipes have not frozen. This is a kind of damage that gets much worse if it happens when no-one is around to mitigate it. You would also want to keep mail from piling up outside the house.
In an apartment, there will probably be no visible signs you are away. If your mail is just put on a table or the like, you should ask a neighbour to collect it for you (and bring them a small present back as thanks) or make arrangements with the post office. If you get a newspaper delivered (I know, how quaint) get the delivery stopped.
Statistically, your vitally important possessions will be no safer from theft or fire at someone's attended home as at your unattended rental place. Maybe your place is more likely to be broken into, but theirs is more likely to burn down while they cook or something. Both cases are supremely unlikely. It's not a bad time to do some backups though - take a DVD or external hard drive of pictures, documents, scans of important papers etc and leave that with family or friends.
Don't leave anything in the fridge, like milk, that will have spoiled by the time you return. The freezer should be fine, as should things like jam and pickles that people routinely leave in the fridge for months. Check your counters for apples or other food that will get moldy over a period of weeks.
Finally, tidy up so that if anyone has to go into your place (perhaps the super to make repairs, or family that you've called and asked to get something you forgot) it's not embarrassing. Make sure everything's clean, and private things are put away out of sight. Close all the curtains to keep it cool (or warm) and to make it less obvious you aren't inside. Double check all the windows are closed and latched. Leave all the doors between rooms open to let air circulate. Turn off the lights to save electricity; you might put one living room and one bedroom light on a timer to simulate being home, though this is less important in a building with many units.
Make a list of what you now don't have and might want on your frst day - milk, cream, bread - and take it with you. If you remember to stop into the store and get these on the way home from the trip, you'll arrive happier.