Straight pool (14.1) has always been my favorite. It requires every skill in pool, with high demands on precise position and patterning. It's also rewards creative thinking and imagination. No other pool game requires such sustained concentration, which can certainly be draining, especially on a tight pocket table, but the focus required to play it well is deeply satisfying.
Eight ball can be a fascinating game, too. Like straight pool it requires precise position, patterning and creativity. I think, more than any game other than one pocket, 8-gall is a strategist's game. That, in itself, makes it a lot of fun.
One pocket is somewhat knew to me. I'm taking to it strongly. It combines much of what I enjoy about straight pool and 8-ball, with the addition of many creative shots and traps that neither game offers. This is definitely a thinking man's game.
Nine ball for when I'm too tired to think. Ball by number. It's a great relief sometimes after playing a thinking game to play 9-ball. Good for working on centerball position angles and for practicing returning the cueball to the center of the table. Safetys and kicks can be interesting. Also good for practicing "line positioning," which I use a lot in all games.