I haven't seen
Conquest Games Normans mentioned yet, and in my opinion they could make good fiefdom troops or alternatives to Gondorians, if you're of that persuasion, as would Fireforge minis.
Perry's Sudanese Tribesmen (with bald heads) could make good Mahud alternatives.
It's also worth pointing out that historical minis don't need to be used exactly as they're packaged - converting, kit-bashing, or using them for parts can work out well too. Fin's Gondorians are a fine example of how just a little conversion work, and the right paint job, can pull the minis out of their historical context and make them look right at home in Middle-Earth. I'm currently converting some men of Pennath Gelin by replacing warriors of Minas Tirith's heads with more ornate hoplite helmets, to reflect the great wealth of that fiefdom. While I haven't attempted this last one, it did occur to me that Perry Zouaves with bare arms and shaggy heads wouldn't be half-bad as corsairs of Umbar, either.
As this thread indicates, historical miniatures can provide an abundance of alternatives for many human factions, but the actual fantasy races are a little harder to find good alternatives for (that generally fit the WETA/GW aesthetic). None the less, here are a few that migh work OK:
The aforementioned Vendel fantasy range (available from
Sgt. Major Miniatures) is not bad at all, especially for dwarves and elves IMO. Their orcs and goblins are a bit cartoonier than the LOTR designs, but still much less so than a lot of fantasy miniatures.
Mirliton's Fantasy Range leans towards older, cartoonier minis, but some of the dwarves might be serviceable and the half-orcs would make good orcs or more lightly-armed uruk-hai.
Hasselfree have a few dwarves that would work (I'm thinking Russ, Benn, and the multi-part warriors), and they also sell orc heads on a sprue, which could be put on the bodies of some other minis.
For hobbits, I think the pages
Halfling House Scale Guide and
Halfling Showcase are your best resources, and are fairly comprehensive in terms of what models are on the market and which will fit in with the LOTR range.
From Old Glory, you've got
Terronus, Isle of Goblins, some of which appear to be a good match for LOTR Moria goblins.
Reaper have tons of miniatures, mostly leaning towards heroic scale and maybe more suited for roleplaying, but there are some gems in there if you dig around that would be fine side-by-side with LOTR minis.
The Grey Maiden always struck me as a good female high elf hero sculpt.
Lastly, while not my favorite minis on their own, I have seen some very convincing orc conversions using the
Wargames Factory Orcs for parts (on either this site or TLA), and they are very, very cheap.
I'm sure there are many, many more out there, but the more realistically proportioned LOTR minis can make it difficult to find other compatible fantasy ranges.