69 Here, it works basically as Tord described. At my particular university, they start charging you extra if you've taken more than 140 hours worth of classes (that's semester-hours per week, I guess; most classes are worth 3) before you graduate. So, at 16 hours per semester (roughly the recommended amount), that'd take 8.75 semesters, or five years. So, as long as you don't fail and have to retake too many courses or change your major late enough that you have to take more than the needed amount of classes, you'll graduate in 4-5 years and be fine. However, if you do have to stay longer for whatever reason, they'll just up your tuition some.
As for grad school (i.e. if you've already graduated from a college or university with a bachelor's degree and are working toward a Master's degree or PH.D.)... I don't really know. That's still a long ways off for me.