D&D:
Pro: You’ve got magic, you’ve got elves and stuff, and you’ve got Dragons, oh yes do you have dragons. A campaign where you go around the frozen north and kill dragon after dragon sounds like D&D at its best.
Con: Varies based on choice of edition- pre-4th casters have less magical staying power than Skyrim’s mages; on the other hand 4th edition’s play ethos is largely based on tactical encounters, and Skyrim’s go-anywhere, do-anything sandbox is a major feature. Also, D&D comes with its own setting assumptions, which don’t always line up with Skyrim’s.
Burning Wheel:
Pro: Skills level up as you use them. Seems subtle, but it’s a major selling point towards that Elder Scrolls feel.
Neutral: Need to hack the magic system. But there’s got to be something in the Magic Burner that you find appropriate, and the magical Tax system is pretty close.
Con: Burning Wheel is extremely character focused; Skyrim is exploration of setting. Plus only the lifepaths for Humans really work; Nords only.
Old School D&D/Retro Clones (including Dungeon World)
Pro: Sandbox is what these games are meant to do. Easily customisable to make new races, etc.
Con: Most old-school games are low-magic, and casters suffer. Like D&D, it may not necessarily feel like Skyrim.
Savage Worlds
Pro: Easily customisable. Characters will need a few levels to feel as heroic as what Skyrim offers, but by that point, its a pretty good match.
Con: Savage World’s toolbox approach means you’re doing most of the work yourself. If an Alchemy system like Skyrim’s is a big deal to you, Savage World’s alchemy is much simpler.
Warhammer Fantasy Roleplay
Neutral: Ironically, the selling point here is either a strong plus or a strong minus: you play gritty, dirty characters. It’s not a story about the Dragonborn, but about everyone else, the guards, the thieves, the bandits.