If you've been a loyal customer for quite some time, especially once who carries a revolving balance, call up the company and ask what they have to offer.
Say something to the effect of "I've really enjoyed doing business with you, but I feel that I could get more perks/better interest rate/etc. if I went with another card company. It's too bad that you don't have anything enticing to offer me to stay."
That should sound the warning bells right away. If you carry a balance, even if it is a small one, the card company is making money from having you as a customer. Loyalty is VERY important to them and they might be able to sweeten the deal if they know you are going to drop them. Case in point: We knew we were going to buy a house, so we paid off and closed a few of our lingering 'college days' cards. When we called to close them we were offered so many things, lower interest rates, no annual fees, no interest on transfers for up to 2 years, etc. But, since we were buying a house and wanting to have clean, stellar credit we turned down everything.
You'd be surprised at what a company might be willing to do if they know you're taking their business elsewhere. Don't approach it as 'accusatory', just as an "I've enjoyed being a customer, you've always treated me well, but I have better options". You always catch more flies with honey than you do with vinegar!