I've played fallout 3, Oblivion and now Skyrim. I have never liked or really wanted to play in 3rd person. I tried it a few days ago and wow! Skyrim needs to be played this way. You don't realize all of the awesome animations you miss out on in 1st person. It takes a bit to get use to combat but once you do you see Skyrim in a whole new light. It's easier to see around you and doing things like power attacks and receiving a dragon soul are incredible.
Ugh. All the reasons I don`t play in 3rd person.
I really don`t need to see what I know I`m doing, running, fighting, farting. I know they happen.
1st person is also very immersive, I walk under a bridge, I feel like that bridge goes over my head. Someone looks at me when they attack me, it feels like they`re attacking
me. Also, I have no problem seeing around me or enjoying the beauty of the world, in fact it feels more real running across that landscape or rushing the rapids over a waterfall.
3rd person removes me from that immersion, from the feeling of being there.Let`s not forget that we see everything in 1st person in reality and we can`t go above and behind ourselves to see 360. We dn`t have eyes in the back of our heads, we must turn to see and that`s easily done in 1st person. Strafing and turning is also an essential ability to learn when fighting in 1st person that allows you to see round and fight with good use of audible cues (hearing what`s going on around you).
But I`m sure if people could they`d walk around in real life 10 feet above and behind themselves because of our real life limitation.

But all to their own.
p.s. However I will use 3rd person as a mirror (see how I look) since there are no mirrors in Skyrim.