if you're from europe, check pricerunner and choose either tuesdays or wednesdays to fly on.
These days are the cheapest to travel on (it can be up to 100$ difference from what I've checked).
I did NY for around 600$ (350$ for flight there and back) total for one week (with lots of beer and
shit included) but that was a while ago when everything was cheap (also, I live in Sweden btw).
If you don't have anything against switching flights a bit, you should definately check out these.
Europe = interail card (though it's almost three times as expensive as when I did this, it's still the
way to go if you wanna visiy alot of countries in a short amount of time). Maybe check RyanAir
(10£ from UK to Sweden doh!), if you wanna start the trip in a country far away from yours.
It's really all about picking the times no one else wants to travel on and living in hostels.
edit
Oh! I haven't tried these but asking for last minute tickets is cheaper than taking a cab a few blocks apparently.
You should ask about these at the airport though so if you live close by one of these, you're lucky :P