I would probably just freeze up, and call for someone else to see what would happen if two people looked at him from different locations at the same time. If you could get it to run back and forth between you.
I live on water, ship has enough light to prevent mobs spawning aboard. If i say go on some shore ill prob just kill it head-on. If it has finite hp points and no aoe damage on huge area - means i win.
step 1-find a pumpkin.
step 2-do everything else to survive.
step 3-never make helmets.
step 4-enjoy being endermen proof!
step 5 (OPTIONAL!)-build some houses for the endermen.
step 6-make a sword of at least stone or iron quality.
step 7-kill them and find out what items they drop.
Just checked the Minecraft Wiki to see what the "Enderman" actually was, this is the first time I have heard of this mob. But after reading the info I will just kill it like any other hostile mob, with either a sword or bow and arrows. Even though they are a passive mob and only get aggressive when you look away from them I will still just consider them as hostile and kill on site. I don't bother with Pigmen since they only attack when you hit them, not when you look away.
I have different thoughts on the "Enderman".
1: I think the mob and its abilities are interesting and it is something that I have never seen before in any game I have played. The idea of a mob that gets aggresive when you look away from them is cool. Plus they can charge at you and even teleport. They can pick up stuff and just look cool and creepy.
2: But, a part of me does not like it as it is just another mob to kill and worry with. I am fine with just the Creepers, Zombies, Skeletons, Spiders, Slime, Ghast and Zombie Pigman. Still wish to see a Spider Jockey. I have fun just hunting these guys and don't want to have to worry with fighting Enderman.
But I will hold off my personal judgment and personal opinion on the Enderman. I might really like them when I see them inaction and learn what they drop when you kill them. I apologize for some of the off topic stuff I typed.
EDIT: I did not see anything on the wiki about wearing a pumkin on your head will keep the Enderman as passive. Is this true? Or is it just a joke that someone came up with?
Eidt #2: Nevermind, just saw this from a link in the wiki that takes you to a page on these forums: "It would seem that wearing a pumpkin prevents the new mob from seeing you, although this is unconfirmed at present."
I have 3 solutions:
1) Have a pumpkin on my head.
2) Walk up to it and kill it with a sword or with a bow and arrows from the distance.
3) Stare at it and run backwards hoping nothing will attack me from the back.