Okay, so, I usually ready LotR every couple years, sometimes more than that. Recently I started watching the movies after finishing the book as it allows me to get really annoyed about some major character changes. That aside, I'm sticking with the books almost strictly and ignoring the films. First, which version of D&D do we use to model the characters? Going way back to OD&D, the halfling and dwarf classes are pretty much directly copied from LotR. Frodo wasn't a halfling thief, nor halfling fighter, nor a fighter/thief...he is in fact simply a halfling. Aragorn is most definitely a Ranger, and this isn't introduced until Strategic Review 1-2. D&D then completely ignores the class (along with race-class distinction) and AD&D re-implements it. Basically, we need a version that includes class-as-race as well as some of the more advanced classes. Seems pretty obvious we should just use OD&D, but the rules are nearly incomprehensible and inaccessible. Thankfully, we have Labyrinth Lord: Advanced Edition Characters. Coupled with Labyrinth Lord itself, we essentially have all the advanced classes from AD&D grafted onto D&D without all the stupid rules that make the game annoyingly unplayable. I'm not about to get into an edition war or whatever, but LL:AEC is, to me, pretty much an idealized D&D and the one that retains playability with added complexity. I can't say enough about it. I'm approaching this as if LotR was an actual D&D campaign. Okay, so here we go...
Let's start with the Fellowship itself. Since attributes aren't nearly as important in LL as they are in AD&D (they're almost completely unimportant in OD&D, which really isn't a bad thing), I won't even bother, unless there is something that really stands out. I sort of cheated and looked at the MERP book Treasures of Middle Earth for some of the weapons the characters use. Sue me.
All members: Elven Cloaks. Pretty much directly out of the books. These cloaks also keep the wearer warm/cool as necessary.
Aragorn - 16th Level Dunedain Ranger
WIS is probably 18, CON is possibly 18 as well. I picked 16th level because this is the first level that Rangers can cast 3rd level Druid spells, the primary which is Cure Disease. Aragorn never really seems to use any "spells" except neutralizing poison, curing wounds, etc. This also gives him 2nd level ability with magic-users spells, which makes sense considering he studied with Gandalf for a length of time. If you read MERP 2nd edition, there's a lengthy explanation as to how magic use attracts the Eye of Sauron and other dark powers. Essentially, every time you cast a spell you have a chance at drawing the notice of Something Bad. It's a good justification for the lack of flashy magic. So, yeah, Aragorn can cast spells but he's not an idiot and doesn't. Plus, he does +16 points of damage to nearly all the enemies he'll encounter, which pretty much means he's an orc killing machine. Anduril is somewhere in the +3 range and does +1D10 flame damage to orcs and +1D10 cold damage to undead. Assuming Aragorn has around a +1 bonus due to strength, he's doing a minimum of 22 points of damage to an orc, or 38 points max. Ouch. That's enough to kill an 8th level orc who rolled average hit points. Again, ouch...now we see why no one fucks with Aragorn. Technically Anduril is a Flame Tongue/Frost Brand, but the rules for those sword-types don't accurately represent what it can do so I'm ignoring that. It probably also qualifies as an artifact.
Legolas - 8th level Elf Fighter
No implied magic ability, so he's not of the Elf class. Elven Boots to simulate his ability to move nearly silently. DEX and CHA are 18. +2 Shortbow of Speed, which allows him to fire 3 times per round. For whatever reason, his bow does 1D8 base damage, not 1D6. I guess because it's an Elf bow. Whatever.
Gimli - 9th level Dwarf
CON 18, most likely maximum hit points. STR is high (17 or 18). +2 Axe of Orc Slaying, does +1D10 damage to orcs. Some form of Dwarf ringmail or chainmail which protects about as well as platemail and shield of better (AC2, perhaps as low as 0). 9th level so he can settle the Glittering Caves. Most likely leveled up once or twice during the books, so his level is debatable. Easily the most resilient and dependable toe-to-toe fighter in LotR.
Boromir - 12th level Dunedain Fighter
STR 18, CON 18, WIS is 11 or so...well within the average range but just low enough to make him a bit brash and more susceptible to the ring. Definitely not stupid by any means, though, and absolutely fearless. Horn of Gondor summons allied forces if within range. Sword is probably +1 or something; just because of lineage, not due to being "magical". High-quality Gondorian armor, AC 1 or 0.
Pippin - 4th level Halfling
WIS is average, but he's young and stupid and failed his Save against the Palantir. STR 18, the biggest, strongest Hobbit in history. +1 dagger/shortsword. Gondorian armor is around AC 1.
Merry - 4th level Halfling
Smartest of the bunch, INT might be as high as 15 or 16. +1 dagger/shortsword. Rohanian armor AC 4.
Frodo - 5th level Halfling
WIS 18, mithril chainmail grants AC 0. Sting is a +2 shortsword of Orc Slaying, +1D10 damage to orcs.
Sam - 4th level Halfling
WIS 16 or 17, CON 17. Oddly enough, Sam is probably the best overall Hobbit fighter in the books when he's pushed into it. He's essentially incorruptible, seems like he automatically makes all saves versus any sort of mind-altering effects. Either that or his player has a loaded D20.
Gandalf - 20th/14th/20th level Maiar Magic-User/Druid/Cleric
All stats 18+, knows and can cast every spell. Gandalf is actually an Immortal, and thus cannot cast any spells without pissing off a bunch of other Immortals. Has a bunch of artifacts, including a staff, ring and sword. Essentially a high powered NPC who aids the PCs in the beginning then fights an unbeatable DM meta-plot monster as a way of being removed from the party. Until the end of the books, when he shows up again and saves the day. Good job, Mr. DM.
What's interesting is that D&D can actually recreate a pretty good LotR game fairly easily, as long as the players don't want to cast any spells or be anything other than fighters. Quite honestly, though, I think those sorts of games are a lot of fun. I played a fighter in my first D&D game, and the other characters were another fighter and a chaotic dwarf. None of us thought the game was lacking at all due to the inability to cast spells or heal or any of that crap.