I usually don't make a lineage or recycle characters from other games in the series. I like to make a diverse set of characters that have completely different backgrounds and characterisitcs. It keeps the games fresh because they each have different perspectives. Skyrim will be no exception.

In Skyrim, two of my characters will have the same name as two of my characters from Morrowind. Noctis, who is a Bosmer thief, and Gelidian who is a Dunmer mage. Perhaps I will add a random number after their name to make them descendants. I don't know which if any I will make a secessionist. I will have to play first to decide.

Maybe I will quickly throw together another character for my barbarian in Skyrim.

Typically, no, as most of my canon characters never really hook up with anyone, or live long enough to come back in another game. There is the potential that this may change come TES VI. Depending on how long this game takes place after the events of Skyrim, I may either use my Dovahkiin again, or play as one of his children/grandchildren.

Yeah my Dunmeri Vampire Slayer (Deus Garoth) in oblivion is the cousin of the Nerevarine, and his son is the Dragonborn (Ulmer Garoth).

The ages of Septims agent and the Eternal Hero are set; He was 5 when Septim's agent was born. 10 years go bye between daggerfall and morrowind. Also, there is a 6 year difference from the start of Morrowind and the Start of Oblivion. So they couldn't really be directly decended, although the same guy really could've done arena (being 63 by Oblivion.)

EDIT: pointing out that Septims agent dies

Ansestry is much more possible for skyrim.

No, but I've come up with a death for my Oblivion character. I've grown quite attached to him!

Can't say I ever do lineage, however I've played most of my characters in both Morrowind and Oblivion. With a mix of mods (recently started to PC games) and some imagination I can role-play them through all three games (I've never really got into Daggerfall or Arena).

I would feel like my family was stuck in some sort of temporal flux, each one living out the same fate of saving the world.