Interesting so far, I don't think anyone has picked a caliber newer than 60 years old and, except for the 104-year old .375 H&H, I believe only one poster has picked a "magnum."
The 375 H&H would definitely work. However, it's overkill for most things. The 338 probably is too, but I wouldn't consider it a non "magnum"... It's one of my favorite cartridges and works well...