I took 4 AP classes, 3 in my senior year; Bio, Calc, English, and US History
I had the exact same thing, and those were all the AP classes offered at my school. The 3 in English got me nothing, surprisingly, and a 4 in History took care of my entire requirement. I got a 5 in Biology, which counted for 12 hours (three lab courses), but since I was in aerospace engineering, it only got me free electives.
I got either a 3 or 4 in Calc, which would have given me credit for the first of five Calc classes, but I decided to go ahead and take Calc I anyway, in order to better help me learn the way things were done there.
One thing that annoys me to no end (even though it's been 20 years now), is that many high schools counted AP classes as a max of 5.0 on a 4.0 GPA scale. My high school only counted it as a 4.0, so at least within the high school system, the extra work didn't count for squat over someone else in the main track courses.
Like Digits said though, I would also recommend someone take AP classes if they can. Most of the time, they only count towards those core classes that all majors have to take, but for most people, getting those out of the way early will help you concentrate on your actual major classes.