The classic D&D troll, re-dubbed the "Hill Troll" in the Lands of Ara.
There are three main influences / factors that steered me away from using standard D&D trolls as written:
(1) Crimson Blades of Ara. Trolls as they appear in Ara were first conceived for a non-D&D game, i.e., my homebrewed system Crimson Blades of Ara. The main idea put forward in CBoA that impacted my choice to expand trollkind into a whole family of related-but-different monsters was its conception of indigenous Arandish monsters vs. extraplanar, summoned ones. Trolls were one of the few indigenous Arandish monster races (along with dragons, giants, and the undead) -- and therefore seemed to need to come in many regional varieties. In fact, CBoA sported even more trollish types than I now use in the Labyrinth Lord iteration of Ara, including (in ascending order of power) mud trolls, tree trolls, hill trolls, rock trolls, and swamp trolls. (Maybe one day I'll stat out those first two types for Labyrinth Lord.)
(2) The works of J.R.R. Tolkien, wherein orcs, goblins, and trolls all seemed much more powerful and dangerous than they did as statted for D&D. To be fair, D&D trolls are not much like the trolls who appear in the "Roast Mutton" chapter of The Hobbit -- the former are thin, rubbery, regenerating things, while the latter are huge, ravenous, turn-to-stone-in-sunlight type things. But nevertheless I felt from an early age that trolls -- or at least some varieties of trolls -- should be more powerful and dreaded than the standard D&D troll.
(3) Tunnels and Trolls. Although I did not consciously realize this until quite recently, Ken St. Andre's Tunnels and Trolls surely influenced my outlook on trollkind. For example, on p. 2.7.2, in the description of the troll that inhabits the included introductory adventure "Trollstone Caverns," St. Andre writes: "This is a Cave Troll of the classic type -- direct sunlight will change him into stone." Not only does this passage align this particular troll with Tolkien's conception mentioned above (and perhaps explains why so many mythological trolls live under bridges and the like), but it subtly implies that the "Cave Troll of the classic type" is not the only type of troll available. I could also swear that the words "rock troll" appear somewhere in the T&T rulebook, though I cannot now locate the reference.
Now, where exactly I got the idea for the swamp troll and the rock troll, I do not exactly know. However, I can tell you precisely what creature from pop culture LOOKS the most like a rock troll: the H.R. Giger Alien creature.
The elongated head shape of the Alien is not quite right, nor do Arandish rock trolls have that little mouth-within-a-mouth thing, but in terms of overall stature, way of moving, and relative invulnerability, rock trolls and aliens are indeed closely related.
Swamp trolls, which dwell mostly in the Great Western Swamp, and which constitute the only trollish strain to eschew walking bipedally, remind me somewhat of oversized, aquatic bulettes. A direct influence? I cannot say now, but it is a strong possibility since bulettes are (and have always been) a particular favorite monster of mine.