It varied by playthrough. My Red team had Snorlax in it, and I recall using Aerodactyl as my Fly user for a while. In gen II, I've used Eevee, Lapras, Togepi, and Snorlax on my teams before.
I've never been a big fan of Shuckle, and it generally arrives late enough that I don't feel compelled to use it. I don't think I've ever bothered to use the other fossils (Kabuto and Omanyte lines) on my team, although I've used them in newer games. I don't think I've ever used the hitmon line for anything other than Pokedex completion purposes. I recall dragging Sudowoodo to the Elite Four the first time I faced them in Gold, but I didn't really have a team (just my unevolved Totodile and a bunch of HM slaves), so Sudowoodo was my buffer for reviving Totodile.