Some colleges cap the number of enrolled students to a fairly low number.
I believe UChicago’s Core classes are capped at 19. These Core classes comprise over 1/3 of the undergraduate program. Some lectures or introductory non-Core courses would be much larger, but overall, > 75% of classes have < 20 students (according to UChicago’s USNWR profile). Most other top ~20 private research universities claim high percentages of classes with < 20 students, and also can boast of distinguished faculty rosters. Nevertheless, you might find that many intro classes, pre-med classes, or intro-intermediate classes in popular fields are rather large even at some of the most selective colleges.
If you want consistently small classes, your best bet usually is a LAC. Even some very selective LACs will have some popular classes with 50 or more students. Colorado College reports an average class size of 16.3 students. It officially limits enrollments to 25 unless there are 2 professors, in which case the limit is 32 … but “very occasionally” exceeds these limits to accommodate student demand. You’d need to do some digging to find other colleges with actual class-size caps (as opposed to low averages, which can be driven down by large numbers of advanced classes in arcane subjects). A very low figure for the number of classes with >= 50 students may be a better indicator than a very high figure for the number of classes with < 20. Ivies and peer private research universities typically claim < 10% of classes have >=50 students. Top LACs typically claim < 5% of classes have >=50 students.
Here’s a thread that compares class-size distribution claims:
http://talk.collegeconfidential.com/college-search-selection/708190-avg-class-size-p1.html
It’s almost a decade old, but probably remains a fairly good indicator (assuming the numbers were reported accurately.)
For up-to-date numbers, each school’s Common Data Set, section J, reports class size distributions. Google for [college name] + “Common Data Set”. As ucbalumnus mentioned, many colleges have searchable online course schedules that contain enrollment information. Google for [college name] + [Fall/Spring] + [year] + “courses” (or something like that).