It's happened to me only twice in gaming. Both times were in Halo 3. Both times were online multiplayer and fairly highly ranked (I think the first was a Skill 30 and the second at Skill 40-something). I'm pretty good at halo, and its really the only fps ive ever played online, although i havent played it much. The first time I was playing Lone Wolves, and i was the lowest ranked there, i think i was 30 or 31 and someone there was a brigadier. At the lobby, I'm like, im gonna get pwned... But then once the match started, i just started killing, and didnt stop. I was at 18 kills in a row before all four of them ganked me and took me out. That was my only death. The match finished with me on 25, and the next person on 7. The second time was much the same thing.
It also happened once when I foolishly picked a fight with a guy 3 years older than me and a lot bigger and got in way over my head (this was a few years back when i was the kind of person that'd pick a fight at the slighest thing). I was getting the crap kicked out of me, then in a complete reversal i started to kick the crap out of him. He only hit me once more after that, and i hardly felt it at all. We both nearly got suspended though, so it probably wasn't worth it.
It was strange because, as you say, I didnt realise what was happening till it was over. And like someone said earlier, it is indeed as if your will is instantly transferred to the game. I'm not so sure if it is really possible to enter 'The Zone' at will though, unless you are a zen monk thats addicted to fps. It just something that happens, i think, and you briefly enter a heightened state of awareness. Because, again, as someone said earlier, it doesnt just happen with games. Perhaps it's a point past the 10% of our brain that we all can normally use.