Excluding airfare, you can easily get by with about $800-$900 every two weeks assuming you stay in bargain hotels, hostels and bang/buck restaurants. If you stay in hostels exclusively you can even get by cheaper.
The best way to define your budget is to look at the travel guides focused on budget. My favorites in order of preference are: Let's Go, Lonely Planet, and Rough Guides. Also visit
Hostelworld.com for good prices. Also visit
Tripadvisor.com huge and active forums (broken down by country, city etc) as real experienced travellers discuss the ins and outs on every travel topic under the sun. I've received GREAT advice on cheap places to stay, etc, etc.
Food-wise, it can be VERY cheap if you go to the local supermarket to buy some bread, cold cuts, yogurt, drinks, etc. Supermarkets and department stores in Europe even have really cheap/good restaurants in them if you want warm food. And of course, there's Mcdonalds and KFC. If you plan on going to restaurants on a regular basis, this will sap your $$ much more quickly. Also
REMEMBER to factor in the Euro/Dollar conversion. Go to XE.com to use their up-to date FX calculator.
You can easily pre-budget what you'll need MUCH BETTER than asking your question here.
Do this exercise and you'll know what you need. I've done trips on the cheap at very nice hostels as a student and had a blast! As long as you're willing to go the extra mile, you can make it verrry cheap!!
Don't let money hinder your experience. If you're overly frugal to miss out on things (performances, clubs, events etc), you'll be doing a disservice to yourself by shortchanging on the lifelong nostalgic memories. IMO, if there's ever a time to carry a credit card balance it's when one is one vacation. I've learned this lesson the hard way when I first started going to Europe and missing out on fantastic things (which I later re-visited) b/c I was too damn cheap!
Good luck!