I'd give almost any game a shot if it's free. Even games I've seen before that I'm really NOT interested. Nothing specific comes to mind, but I'm pretty open minded, I would give almost anything a chance. Keyword: almost. Those Babyz games or whatever and others like it might be the only things I would straight up avoid.
However, whether intentional or not, this seems like a question aimed at P2P MMOs. With that in mind, I have a few that I wouldn't play even if free, mostly because I have played them before.
-WoW
-Aion
-DDO (the freemium version doesn't count, it's only 30-40% of the full game)