The puzzle crown has always been hard to win with Tetris still very much ontop but there were a few worthy challengers.

Released in 1999 as a launch title for the Dreamcast, Chu Chu Rocket has you place arrows on a checkerboard in order to guide mice to their rocket all while avoiding the cats, among the regular puzzle mode there is a battle mode for up to 4 players which supports local and online play, one of the earliest examples of online gaming.

You can still play it online through private server rental.

Pros
Works best as a multiplayer
Puzzle mode is decent length
In most cases, this game was free

Cons
Limited appeal for solo players
Unless you're Japanese I doubt anyone had that much success with the Dreamcast online system.

Verdict
Chu Chu Rocket is well missed and I'd welcome it back with open arms