Popular is in the eye of the beholder:
9-ball ... folks like because it's quick. But, the downside is that your opponent can run the first 8 leave you the 9, and you win.
8-ball ... because it's also kinda fast, and you have to win the game, as opposed to 9-ball where your opponent can run the first 8 leave you the 9, and you win. Put's more pressure on you to play well and win (IMHO).
one pocket ... Lots of defense. And, it's (typically) a longer game than 8 or 9 ball.
14.1 ... Real pool game. Demands all of the skills required to be a good pool player. <--- the best game of pool there is.