Waiting for a battle to start would probably be the hardest thing mentally. I would have been horrified at Helm's Deep and in Minas Tirith.
Now when I start to think about it, the Fellowship encountered a huge amount of scary things *shudders*
I think I could go all the way through with Merry and Pippin if I really had to. I'm not sure if I could follow Aragorn, L and G to the what ever end but if I went with Frodo and Sam, the cracking point would be Shelob's lair. Dark and slimy tunnel and then there's that spider... (what spider phobia?!
) I could probably handle the way from Cirith Ungol to the Sammath Naur (I mean mentally. I can't fight or do anything like that) but if I pass out in Shelob's lair and get eaten, it doesn't really matter anymore.