From how far will Endermen notice your gaze?

Solution 1:

According to the wiki, the range is 64 meters.

They are generally neutral. However, if a player looks at them by placing his or her crosshair directly over them for half a second, they freeze, stare back at the player, open their mouth and become hostile. This only happens, however, if the player is not farther than 64 meters from them. They stay frozen as long as the player doesn't move the mouse at all, even if just one pixel.

Solution 2:

I spent a night on top of a town church and antagonised all the Endermen I could see. I could get them to look at me no matter how far away they spawned, though getting the crosshair exactly over them at extreme distances was actually hard and took a few tries to get their attention.

Though it's not an exact number obviously, I can attest that Endermen will notice you looking at them from several chunks away.

Solution 3:

The reason they seem to not notice you is because the place you need to look at them is about half a block above their head. I assume this bug will be fixed in a later patch.