I finally got around to start collecting statistics on custom-client use. There's a page up over here.
Keep in mind that the custom-client "IDs" are self-reported, including the "unknown" ID, which is the default if the author hasn't set anything. The empty ID is an older default. The "hour-of-day" graph is UTC-based, so the edges correspond to UTC midnight. Once more data has been collected (this should be on Friday), I'll add daily use and day-of-week use graphs as well.
Cue all the jokes about default client usage!