First person. Even for party games. MMX and Legend of Grimrock prove it's still doable.

Third person because Gothic. End of conversation.

Seriously though, both can be good depending on the game even if you prefer one over the other. System shock 2 and Deus Ex are two of the best ever (IMO) and they would not have worked as well in 3rd person.

Depends on the game really. First person draws me in way more than 3rd person. I am more able to be immersed in the game in first person. When experiencing a game in 3rd person I just take that view point, "Oh they hit my guy." While in first person I don't have that entity to pass off any surprise, suspense, or emotion upon, which helps me with immersion.

It really depends on how the game is made. Many rpgs are just fine in 3rd person.

I prefer third person because the camera control is generally easier.

Only third-person. You can view your character, you can enjoy looking on his gear and appearance. But I would like to be able to switch between points of view. Sometimes first-person is good for battles.