For a period after 9/11, ID was required to be shown at the gate on domestic flights. I don't recall when that stopped, but it's been a while (and apparently long enough ago that apparently some have never had to do it).
I seem to recall IDs occasionally being checked at the gate prior to 9/11 as well. Memory is fuzzy, but they weren't checking boarding passes or ids at security. But back then I would always get my boarding pass at the check-in counter (sometimes exchanging an actual ticket for the boarding pass).
I spent some time looking for old information, best I could come up with was this article [1] from 1996 about requiring photo ID at check-in, which doesn't mention checking at the gate, but does mention why the airlines might be happy to do it (protect revenue by making sure passengers don't fly on other people's tickets... unless they share their name with the other person). This article [2] , also from 1996, is a little bit less precise about if people are denied at check-in or by gate agents.
I think it's all quite hazy, because if you had no checked bags and it was a small airport, but you might just go to the gate and try to get your boarding pass there. That and 24 years have passed. :D
