D&D:
You could say the earliest D&D art was unnecessary, the scrawly 70s home-made stuff. I mean: everyone knows what a dwarf looks like. But the earliest work was so primitive it communicated a useful message--anyone can do this, get out a piece of paper and start making things.
By the early 80s, some of the art was doing genuine work--you had not just Erol Otus' lurid cartoon-expressionist mood-music but you also needed that picture of a beholder to know what a beholder looked like or know what a beholder even was, really. The Monster Manual-era stuff also imparted a
culty, grimoire-like, almost medieval tone to a lot of D&D that it held onto until 2nd edition.
Around 2nd ed, the mainstream D&D worldbuilding art had been done and basically D&D art was just a showcase for whatever the mainstream and best-of in fantasy illustration was that year.
The exceptions were Brom over on Dark Sun (though as much as I like Brom, a lot of the early Dark Sun stuff had an S&M gladiator aesthetic that made the whole thing seem way too WWF for me for decades) and Diterlizzi on Planescape (though I wish they'd let him do the covers). Spelljammer seems like a missed opportunity--the art direction was at odds with
what the setting could/should have been. Where was Moebius when they needed him? Off getting paid more by someone else I guess.
This state of affairs--D&D=whatever mainstream fantasy is--has gone on more-or-less pretty much the same until the present, with a brief detour to make warforged look like they fit into a fantasy setting and with Wayne Reynolds on D&D and Pathfinder showing western audiences something eastern ones had known for years: you can do D&D as an anime. Other than just sitting on the page looking good, the main long-term effect was to broaden out the possibilities for PC costume design and, eventually, give Pathfinder a distinctive look. Though I don't really like it when Path hires other artists basically to work in Reynolds' Kubertish style.
Warhammer:
The job of Warhammer's art was probably the hardest in the history of RPGs: convince everyone it wasn't a D&D clone. It worked though: John Blanche & co were just talented, weird and grimy enough to do what the competition (Runequest, Tunnels and Trolls, Rolemaster, etc)--despite rules just-as or even more different--never did.
An important part of the early Warhammer aesthetic was that it didn't depend on Blanche--he had the best collection of artists ever gathered under one masthead backing him up: Ian Miller, Adrian Smith, Gary Harrod, and Jes Goodwin plus a host of other water-carriers who could reliably be told "Just copy John" and turn something around on a deadline.
Probably had something to do with the Thatcher economy forcing geniuses to work cheap.
The other thing about the Warhammer aesthetic was, since everything had to be turned into miniatures, it not only had to involve style but invention--monster beaks and armor designs these toothless maniacs drew in their garages while listening to Amebix are still being cast in lead to this day.
All in all they've effectively Marvelled D&D's DC for years based on a career system, a crit chart and the work these guys did. And unlike D&D, Warhammer got into space quickly, convincingly, and with a style all its own.
The new 40k-inspired RPGs hold down the fort and a few of the new artists are very good, but I haven't seen much that was jaw-droppingly new out of them.
Warhammer art's ultimate revenge on D&D came in the form of its influence on a videogame called Warcraft which got turned into a somewhat bigger videogame called World of Warcraft, which made the Games-Workshop big chins/straps/shoulder-pads aesthetic (or a telephone version of it) into half the fantasy mainstream. (Peter Jackson being the current other half.)
Vampire:
On the other end of what good art can do, the old Tim Bradstreet pictures sold Vampire: The Masquerade, gave it a distinctive style (basically The Lost Boys done punk-show flyers) and then let the writers do the rest. Which, considering it mostly had a not-terribly-distorted modern setting, was about as much as you could've expected.
A Tim Bradstreet picture told you everything good about Vampire and nothing distinctive. Which worked pretty well in doing what mid-80s D&D had done with fantasy: just lassoing the whole genre in broad strokes so nobody else could claim it.
I never got into White Wolf so I have no idea if anybody else involved kept the quality up, most of what I've seen seems like Bradstreet lite or an echo of whatever Vertigo was doing. As are many of the pictures in the post-White Wolf indie games.
Pretty much the same thing happened with the artists on Shadowrun, only instead of stylizing the real world, they stylized Blade Runner with orks. I'm not sure any one of them really broke out into wholly new territory, but the first edition is the only one I know well.
Call of Cthulhu:
It's a testament to the power of Lovecraft's prose and vision that Call of Cthulhu's lasted almost unchanged for decades with no really iconic art and, frequently, art that worked against it. There are some great Cthulhu images (the cover of the 6th edition is pretty much sublime) but for the most part CoC art is stumpy, turnip-nosed investigators getting tossed around by rubber tentacles.
Visually, it has probably survived on the fact that fans have so many other sources to draw on for imagery. The CoC internet fan habit of passing around creepy old sepia photos and being all "This is totally going in my next Cthulhu game" has probably contributed more to the game's visual identity in players' minds than anything actually commissioned by Chaosium.
There are two other factors in Chaosium getting away with it:
-The Cthulhu monsters benefit from being vaguely or variously defined. Having one artist dominate the game's interpretation of the mythos probably would've made the gameworld seem more its own thing than a vehicle for telling whatever Lovecraft stories you can dream up.
-Like Vampire, the CoC settings are--with the exception of a monster or two--the real world, so players can imagine what's going on from real life and the movies. A lot of games made these days can coast on this: Many indie games purposeful have no style to speak of--they don't need it, the Tarantino bank robber in your head probably looks cooler than the one they could afford to have someone draw anyway.
RIFTS and Palladium:
Man, Palladium had some sweet art in with that seriously boring graphic design. Overslick Kevin Long was always my least favorite, but his ability to describe weird shit in crisp, technophilic detail turned things like Skelebots and Glitter Boys from piles of numbers into solid objects in players' minds. The ones I liked best were guys like Larry Macdougall and Jim Lawson, who took boring things like "regular guy mercenaries" and "another goddamn picture of Michaelangelo with numchucks" and made them memorable.
Considering the unoriginal and creaky rules underneath all this stuff, it's safe to say everything Palladium has or ever had commercially is a testament to the power and limits of "an artist makes a whole world consisting solely of stuff they wanna draw" as a dominating principle.