I used to prefer third person perspective almost exclusively, but now I think that it depends on a game. Many shooters feel more intense when played in first person, but games like GTA on the other hand feel much better on third person.
But in the end the best solution is when you can choose. For example in Fallout or TES I like to use first person in combat but when I'm traveling I usually use third person. So, both it is.
I love both systems as they both serve a different function and give particular perspective. When playing RDR, the cinematic view of 3rd person is great. You see the horses, man on horseback pointing and shooting. Seeing all the action as a spectator in 3rd person is perfect.
Playing first person in Fallout or Skyrim when you are constantly looking for things to acquire such as potions, tools, materials etc, makes more sense. Also, when you are RPGing, using a voiceless character, say in Skyrim, you are the first person and there's a level of immersion there. You are the character as opposed to a puppeteer, controlling the action in a game like GTA.
Games like Deus Ex do a great job at blending 3rd person and first person. So, basically, you walk in the first person, interacting with computers, opening doors etc but then when you climb, latch on to a wall for cover or need to interact with a wall for cover or jumping over it, it's 3rd person. It was a little jarring at first for me but it's done really well.
3rd person offers a cinematic quality and obviously more rounder view. How about Splinter Cell, hanging from a pipe on the ceiling and scanning a room for enemies? Anyone that ever played with action figures will kind of adapt to the 3rd person model pretty well. First person is great when you need to interact regularly with the environment, opening doors, collecting items, hacking computers, grabbing potions, searching rooms and shelves etc.