I have had a Discover Credit Card for over ten years, and I really like it.
I must admit that I am very conservative when it comes to using credit cards. I use them for the convenience of not having to put out cash at the time of the purchase. When my statement comes, I always pay my balance, so I never have to worry about finance charges. There are no annual fees to worry about with Discover, and one thing I really like about my Discover card is the cashback offer. A small percentage of your purchases will go towards getting cash back on your anniversary date (the date you first got your card). The amount you get back depends, of course, on how much you put on your card. The more you put on it, the more you get back. I usually use my card sparingly, so the amount I get back is not very large, but it is still a nice incentive.
I have never had any problems with my Discover card, but as I said, I am a very conservative user, especially now in these tough economic times.