Is there a limit on how high they can go?
There are laws against loan sharking, and I suspect that credit card companies would have to obey them. I suppose it differs everywhere, but for example in Alberta I think it’s in the neighbourhood of 100% PA.
California Usury Law, summarized
So yes, in California, at least, there is a usury law that limits the amount of interest one can charge.
A lot of exemptions, aren’t there? A good reason to check your state’s laws before you scream “YOU FILTHY USURER!” at your bank manager. 
I couldn’t have said it better myself.
Sorry. I didn’t see the part about credit cards. Here’s an interesting link on how usury laws apply to credit cards:
Usury laws offer diminishing protection for credit card holders
Interesting, no? Check your local laws.
If you ever go over 60 days on American Express without paying in full, they will hit you with a whopping 35% interest (for the amount over 60 days, not annualized). But they just call it a “penalty”. I’ve had this happen a couple of times for a number of reasons, and it’s never pretty. I guess they can do this since they are not technically (by their definition) a “Credit Card”, since you owe them everything as soon as the bill comes due.
Reminding me of a scene from “The Simpsons”
Read Credit card issuers right at
home in states with few rules, and State usury limits. They’re copyrighted so I won’t quote. One point they make is that card issuers in lender friendly states like Delaware or South Dakota can charge you, in California or Maine, interest as allowed in their home state.
[soapbox] [slight hijack]
We were with an unscrupulous lender, shall we say, called, of all things ‘Chevy Chase Cash Rewards’. My wife signed up for it and in the beginning it was rather a medium priced credit card (15%). Then lo and behold in late 1998 I guess they hit a rough spot and began ‘holding’ up payments and posting them late to increase their revenue. We had proof of this later, but at the time we just suspected it. They had a grand scheme going as they only hit people with $5000 balances or above. Figuring, we finally surmised, that those people were probably not going to complain because they probably didn’t have the wherewithall to pay it off. Then, they began increasing the interest rate, from 15 to 16.5 to 19 and so on. Our’s finally topped off at 27.8% before we finally paid it off. With the help of Ralph Nader we finally filed a class action suit against them and they failed to show up for the trial. Said there was a sale of the company in progress, which in fact there was. They finally sold out to First USA, another crooked CC company.
[/soapbox] [/slight hijack]
It’s the same rate everywhere in Canada - it’s a criminal offence to charge interest rates over 60% p.a. See the Criminal Code:
I have a Texaco card that allows ATM withdrawals and a running balance as high as $800. The bill shows many numbers including an “APR %” that changes month to month but is occasionally above 100% and has been 116%. Needless to say, this one just gets paid off every month.