beyond the list
Allison and the UHC have come up with a pretty comprehensive list, but here are a few additional suggestions:
First off, does your project require you to go to the countryside or will you be staying in UB? This will determine the amount of nice clothes you'll want to bring (though of course you need at least one nice outfit), if you'll want a water filter and other necessary items, and what types of gifts you'll want to bring (your advisor in UB has slightly different taste than the herdsman you interview for an afternoon).
Second, ziploc bags! You most likely aren't going to eat out every meal of every day, so the grocery store becomes your friend. But wait, you've bought a huge cans of peas (making sure you get all those veggie nutrients, though of course you brought vitamins)! How will you preserve them? Plastic bag and into the fridge. You can get by without them of course, but they don't weigh much and can come in handy.
Third, extra socks!!! They will get dirty and disgusting quickly. You will not want to do laundry that much, yet clean(ish) socks are an important thing to have. Bring more than you think you will need. You'll probably lose some as well.
Fourth, if music is important to you, bring music! Also, make sure you bring things you like and a wide variety. It will be the only noise besides your groupmates talking for a long long time. You know yourself best, so think it over.
Fifth, books! You probably will not have a TV. You will want some down-time. This can be a great opportunity to finally read some of those classics you always meant to. However, make sure there is some coordination. Having repeat books and "the mystery book that everyone thought someone else was bringing but didn't and now everyone really wants to read it" is unfortunate. Variety is also good, every now and then you just want to relax with some mindnumbing action novel or vampire erotica. Again, plan ahead.
Sixth, realize that bathrooms on this trip will 98% of the time not be like bathrooms in the United States. A large percentage of bathrooms will require you to bring your on toilet paper and hand sanitation. If you must have your purell, stock up on it before leaving. It's easy enough to buy wet wipes in Mongolia, but hand sanitizer is not cheap.
Seventh, so you are vegetarian. You are not going to die; fruits and vegetables actually exist here. So do not think you need to bring cans of soup or something. Use that space for something else. Ramen is always available as well. There are two vegetarians on this 2007 trip, so if you have any questions I'm sure they'd be happy to help.
Eighth, mental openess! This trip has a lot of great experiences and a lot of really weird things. Be willing to get out there and push your comfort level. You don't have to like everything, but try it at least with a positive attitude. You'll have a blast, promise.