Note: This answer applies to Minecraft 1.4.1 and earlier. For newer versions see the other answers.
Mobs can not follow you through a portal. "Follow" meaning continuing a pursuit by entering the portal after you do and chasing you again once you're on the other side.
Currently, the only danger coming from the existence of a portal is the possibility of a Ghast spawning by it in the "Earth", "Overworld" or whatever we now call the main area of the game. The space they need to spawn there is at least 4x4x4 and, according to Notch, their appearance near the portal is "extremely uncommon".
As has already been said, you cannot build a portal in the End.
However, they can still be hacked in and used. Using creative mode and INVEdit, I located a naturally spawning End portal frame, and traveled to the End. From there, I placed a portal block and traveled to the Nether. Finally, I placed another portal block and was spawned back on the Overworld.
End Portal: (-1007,16,-123);
End Spawn: (100,53,0);
Nether Portal: (89,64,-21);
Nether Spawn: (11,62,-3);
Overworld Portal: (8,46,20);
Overworld Spawn: (74,64,163);
Note than when I spawned in the Nether, I was inside other blocks and no Overworld portal spawned with me. Spawning back to the overworld worked fine.
Best Answer
Yes, they can.
Here is a link to a youtube video showing it happening.
This is also referenced in this wiki