Yes (typically) only on base miles. For a 1000 mile trip you could get 100% elite bonus (1000 miles) plus a class of service bonus (e.g. business class = 25% for 250 miles) = total 2250 miles (bonuses and base miles).

Non US airlines have different bonusing systems. In 1998, Air Canada gave 10000 miles at every 10000 miles threshold once at 50000 status miles and beyond (=100% bonus after 40000 -- not as rewarding as U.S. system: you don't want to be 100 miles short of the next 10000 mile threshold). Air Canada had several special promotions that made up for the loss of those bonus miles on the first 40000.

Rudi pointed out that class of service bonuses on Lufthansa (in Lufthansa's program, not their partner's programs) are 100% for business and 200% for first class.