I've used a couple and despite what some people have said I never had issues with any of them once i fiddled with the calibration in the FF14 gamepad config:

Xbox 360 Wired Controller
Logitech Wired Controller
Logitech Wireless Controller

I have also heard good things about the official controller but haven't tested it myself.

The only major controller problem I've heard of is that the 360 Wireless controller will not reconnect with the game if it turns off due to inactivity, forcing you to relog.