It depends on your tastes.
If you're staying in hostels, you should budget around $20 in lodging with some bumper room for times when you can't find a hostel and have to stay somewhere nicer (or for when you're just sick of sharing a room with a zillion other stinky backpackers).
You can cook your own meals for probably $10 a day or eat street fair for probably $25 a day, except in the UK where everything is more expensive. Booze budget is personal. I didn't drink a ton while I was there mostly because I was a single female backpacker the majority of my trip, but some folks run up quite a tab fast.
You will have to consider airfare. It is often cheapest to fly into London and use it as a hub for cheap intra-European airfare. For cheap flights inside of Europe try RyanAir or Easy Jet. Outside of this, a Eurrail Pass is an exceptional deal for both price and ease of use. You'll save money on trains, which is usually the easiest way to travel on the continent, and you'll have the ease of not having to negotiate for train fares when you may not speak the language. It allows you to just hop on and off most trains at will, which is very nice indeed.
Budget for museum fees, bus fares, subway passes, say $15-20 a day - you will often exceed this, but will also often not use it at all. If you're a student, be sure to bring your student id from your college or better yet get a Student Advantage International Student ID card for discounts on practically everything.
Souvenir budget is up to you. Keep in mind that you have to carry what you pick up unless you mail it home, which gets pretty expensive pretty fast. Still, you may never have the chance to do something quite like this again, so feel free to live it up!
If you want to do adventuring in Interlaken or other places, you'll run up a tab fast. Interlaken was a blast and must see, but tourist heavy. It was worth it for me just for riding a scooter up in the Alps, but I'm not the hang gliding type.
Have fun! Bring your credit card!
