My wheels are locking up, is it a problem with my brakes?

I have a '98 Altima with power (but not ABS) 4-wheel disk brakes. I'm not sure if something is wrong with them or what. Not too long ago, a car in front of me slowed down suddenly to make a turn, and I hit the brakes moderately hard to slow down as well, and the wheels locked up and I skidded! Also, today, I was approaching a traffic light which turned red, and I decided to stop. Suddenly, I heard the nastiest screeching of tires, and I looked around thinking, "Where's the accident at?" and then I realized that it was MY car that had skidded to a stop. Now, I'm sure some of you are thinking that I haven't been paying attention and I'm just slamming on the brakes at the last minute or something... but really... I'm not slamming on them that hard!!! I think something is up with them. My car should be able to stop: not skid. The tread on my tires seems ok. Could something be weird with the brake lines? Is it expectable for a non-ABS car to have such dramatic skidding on sudden stops? Other people I know *really* slam on their brakes all of the time (harder than I do) and their cars stop just fine, and the tires don't squeal. And let me just say that I try to drive carefully... it's not as if I'm wreckless. So please don't give me a lecture on aggressive driving because that's not it... I just want to know if something is up with my brakes.