I recently had the 100 amp service line to my house repaired but a friend worried me when she said she couldn't believe my electricians didn't suggest upgrading to 200 amp service since I have central air. Is this a common concern or is 100 amp service typically enough to support central air?

All depends on the calculated connected load of the service. If a home is small,or has few large electric loads,the AC could be fine on a 100 Amp service.

I get the AC has been on this 100 service for some time, and the service has been operating fine all along. Now that is not the final answer. To be sure, have an electrician perform service rating load calculations.