What i mean by "break up with them" I mean Give them the "it's not me, it's you" Routine. While I wouldn't ever recommend to do this with a date... It works really well with credit card companies. Call them up and let them know you would like to cancel your card. They're going to ask you why. Just let them know that you're unhappy with the current interest rates. And that there are hundreds of other offers out there that are much better than what you're currently getting. 9 Times out of 10 they will put you on hold. talk to their Supervisor... Or whoever it is that they "talk to" and they will let you know they're willing to make an exception to keep you as a loyal customer.
Thats the rough rout to do. There may be a change that they say "okay, lets cancel it" In that case I would just let them know.... Shoot, I still have a balance. Let me make my last payment and i'll call back later to cancel it. I'll admit. It might be a little dishonest. But if it's the difference in 15% or so in interest its well worth it. Sometimes you just have to play the game.
On another note. There are several cards out there with 0 interest like The Chase Slate card and several AMEX cards. Try not to hold a balance. It's just not that smart. But if you do. I would recommend Slate. Or Even Discover One. Is a good option