I can think of three things right now, (they were when I was a lot younger):
1: I always used to get stuck in Cerulean City for some reason, and so I would level grind. Needless to say, when I finally found out how to "escape," I had a definite advantage over most other trainers for quite some time! :P
2: I think I used my Master Ball on a Snorlax (not as bad as some other Pokémon, but still...)
3: I had a bunch of Ponytas, Rattatas, etc. in my PC (remember, this was the Gen 1 PC system), so, instead of sorting through that difficult, confusing system, I just restarted the game (I didn't lose much, at least!).
Also, I'm not sure if this would exactly be facepalm worthy, but an interesting experience from Emerald:
I actually beat Tate and Liza with my Vigoroth that used DynamicPunch. Yep (then again, Solrock and Lunatone don't have Fighting-type resistances).