I've never actually thought about it while playing games, I'll have to try and remember that for the next time I play an RPG. I know that I always play the characters as though they are me when making decision and whatnot in the game. I'm also not good at playing characters that act differently than I would.
No camera view is as immersive as first person is. It's basic.
3rd person : you control a character you can identify with, and watch him interact with the virtual world through your commands.
1st person : your screen becomes your vision and your control devices your hands. Everything that happens to your character is directly aimed at you.
Just play Splinter Cell and Thief, the immersion difference makes no doubt.
Now of course this only applies to most game genres where you control and make a single character grow, such as : Western RPG, FPS, Stealth.
Every time I've made characters in books, played them in games, or daydreamed about interesting fictional characters, they are all some representation of myself. I realized this quite a few years ago, so lost a lot of interest in writing (I've wanted to write a novel or two), however I'm also objective enough to realize it wouldn't actually limit me anymore.
The last game I played was probably something like Xenon 2 in like 1989, on a CGA monitor. That had a spaceship and flying slugs. There were no multi-views, just flying slugs and a strange alien arms-dealer at the end of each level.
It was then I realized that the era of gaming had reached an early zenith, and quit after that
I always try to imagine myself in real-life in a third person perspective. Kilgore is running low on mana. Must cook pale soggy hotdogs to gather strength and add skill to my skillet handling. Kilgore is confronted with an enemy player. Should he calmly persuade the aggressor to move or bash him in the head with a frozen fish? This enemy is a higher level but if kicked in the knees, his shield fades, and there is time to strike. Kilgore is tired; sleep increases stamina. Got a girl pregnant? Restart game.