i.e, the eternal champion, the agent, the nerevarine, the champion of Cyrodiil, and the dragonborn.

Is there any explicit reference to them in subsequent games? If so, how are they remembered? Did they join every faction that was available in their respective games? Is there any canon for their race and gender?

I've just been wondering because the only reference I've seen to any of them in Skyrim is one in the Dragonborn expansion for the Nerevarine. I'm curious as to how Bethesda sees the PCs, or if they just dodge the question.

There are certain references to past champions.

Race/Gender tends to not be specified.

In Oblivion, there was talk that the Nerevarine left for Akavir.

I believe that the in-game book "The Warp In The West" has a few references as well.
http://elderscrolls.wikia.com/wiki/The_Warp_in_the_West_(Book)

Not so much a direct reference to the agent as it was a means of wrapping up the various endings of Daggerfall.