V, VII, VIII, XIII and XIV. For all kinds of different reasons.

V - Most relaxing level grinding. Spend more time thinking about what job to level next than you do actually thinking about anything.

VII - Most relaxing world. I've played this game enough times to just enjoy the feeling of wandering the world on a chocobo or in the Highwind, talking to NPCs, etc.

VIII - Most relaxing zone. Balamb. The music combined with the sea sounds is just perfect for chilling. Also, lots of sidegames and an easy battle system make for easy chilling entertainment.

XIII - I found exploring Pulse with my character-friends to be really enjoyable because of how they run ahead of you, not everything is in a straight line, you can just chill out in certain stunningly beautiful places on the map... yeah, it's great for that kind of thing.

XIV - When all else fails, I love a glorified chatroom and that's what FFXIV becomes when you're too bored to do anything else. It also has a bit of what I was talking about for XIII. Biggest downside? The soundtrack. It can be hit or miss, but over time it grows incredibly annoying to me, so I tend to switch the music off and play something on Winamp instead.

Honourable mention: FFX. The gameplay and characters did not relax me at all, but the hymns in the game can be incredibly relaxing.

Voted for VIII purely because it has the best mixture of the other things mentioned for other games.