The only character I see as seeming truly epic-level is Gandalf (well, the only
good character)... Aragorn, Legolas, and Gimli are all clearly inhumanly skilled, but I probably wouldn't put them far beyond level 12...
It's not that I think most of you are overestimating the skill depicted on-screen: Rather, I think you're
underestimating the power level of D&D characters. An 8th-level character in D&D is already starting to push the boundaries of what seems humanly possible... Level 12 is four times as powerful. Remember, D&D was made with an epic feel in mind -- which occurs well before "Epic Levels."
(For a point of comparison, try imagining the characters versus monsters of various CRs... A Frost Worm, for instance, would probably give the Fellowship a good battle -- they'd probably come out alive, but still use "1/6th of their resources," at least. Looking at the Battle of Helm's Deep... The Uruk-Hai are probably CR 4 each, at most, and there were some normal Orcs in there with them as well, I believe. The commoners were holding their own against them -- they can't be that powerful. You don't have to be that high level before you can totally decimate CR 4 creatures.)
Of course, there's also the fact that neither the books nor movies were
made with D&D in mind, so you probably won't ever be able to find a perfect fit for the characters

You get some nice ones, but that's because it worked the other way around: D&D was designed with LotR heavily in mind.