Are any Skyrim characters carried over from Oblivion or earlier?

M'aiq is essentially the same in all his various incarnations, but he's stretching it a bit as (in Skyrim at least) he admits to the fact that "M'aiq's father was also called M'aiq. As was M'aiq's father's father. At least, that's what his father said." Consequently it can be assumed that the M'aiq of Skyrim is descended from the M'aiq of Oblivion (but given the timeframe, the M'aiq of Oblivion is likely the same as the M'aiq of Morrowind. Unless there were brothers, too.)

As part of the Dark Brotherhood quests, you

obtain a spell to summon the ghost of Lucian Lachance, who appeared in Oblivion's Dark Brotherhood plot.

The daedric lords make appearances in all the games, so they sort of count, I guess. Of particular note would be the daedric lord Sheogorath, who is considered to be

the player character from Oblivion, given the events of the Shivering Isles expansion. This is never explicitly confirmed, however, just hinted at by the dialog.

Beyond that I haven't encountered any. There are a few references to plot points and locations (one of the wrecked ships you can stumble upon, for example), but that's it.

^{Note: The images link to their respective character's UESP wiki articles.}

Night Mother — Oblivion

Source and higher resolution version of the images: Reddit /r/Skyrim post, "A list I made of all the characters that appeared in an Elder Scrolls game before.", by OccupyTamriel; except 'Night Mother' - images are from UESP wiki.

There are two groups of characters that have been carried over to Skyrim.

The first are the Daedric Princes. They've been around since the first Elder Scrolls game, and, effectively being gods, are immortal and still kickin'. Sheogorath in particular (who is implied to be the Champion of Cyrodil from Oblivion) is carried over from previous games.

The second group is composed entirely by M'aiq the Liar, a Khajit character who appears to have been transplanted wholesale from Oblivion to reprise his role as the Dev's Snarkbox. Whether or not this is the same Khajit, however, is up for debate, both because he's a "Liar" (It's in his name! It must be true!) and because the character says:

"M'aiq's father was also called M'aiq. As was M'aiq's father's father. At least, that's what his father said."

Other than that, the games are completely distinct, character-wise.

Edit: As Josh Petrie mentions, Lucian Lachance also makes a reappearance, but as a conjured companion only, not a traditional NPC.