joshi tm: A couple of games that have permanent captures, but will be finished before all opponents pieces are removed: Extinction Chess, Three Checks Chess, Knight Relay Chess, Racing Kings. And this is even side-stepping that fact that under regular Chess rules the game always ends with both Kings on the board - there's no such thing as taking a King.

AbigailII: Oh, I see. Those games also should be removed from the list. Hmm almost all chess games.

joshi tm: Let's see what's left: all checkers variants, some chess variants, Alquerque, Cam(elot), all boats variants (trivial), all Pente variants, all Espionage variants, all Go variants (very hard to capture all your opponents pieces - OTOH, each player has an unlimited amount of stones, so perhaps Go doesn't qualify anyway), Jarmo, Tablut, Tank Battle, (Big) Jungle. Spider variants have the same issue as Go: it's possible, but very hard to eliminate all pieces from the board, but the number of pieces in the hand is unlimited.