I know almost everyone has made at least 1 character in a previous TES game which they duplicated for the sequel. What is your special way of making it seem as if that person actually survived for (Example) 200 years between Oblivion and Skyrim. Perhaps they are a vampire or an old Altmer? Or maybe they were frozen and have just thawed.

In Oblivion i came up with the most outlandish (yet awesome) character (HEAVILY inspired by Warhammer 40k) and they retain their exact existance from then to now.
Name: Khorne
Race: Daedric Prince (Immortal Form), Breton (Oblivion Mortal Form), Dunmer (Skyrim Mortal Form)
Style: Daedric Battlemage/Dremora
Bio: Khorne was once a Daedric Prince of a similar dominion to Mehrunes Dagon long before the earliest battles of man and mer. He is the Prince of War and Rebellion, and so he waged battle against the other princes and proved the stronger. Eventually in a desperate attempt to save themselves the princes joined together and locked Khorne away in the deepest reaches of Dagon's Realm for eternity. Mehrunes took his throne and commanded his powers for his own will.
20 years before the Oblivion Crisis Mehrunes was preoccupied with his coming invasion giving Khorne the window he needed to escape. But his powers belonged to Dagon and so he could not return to full strength in Oblivion itself. He used what little power he still retained to strike nirn and place a single ember in the destiny of man. Through this a Breton child was born with skin as red as a Dunmer's eye, under the sign of the Atronach. This child, though unusual was no different than any other.
He grew up with dreams of glory and so after his 20th birthday he attempted to become an adventurer and journey into the landscape of Cyrodiil. There he was attacked by mere bandits and upon spilling the blood of one (his 1st kill) he was made an open vessel for his true creator, Khorne who invaded his soul and became his form. Khorne slaughtered the rest of the bandits and took their souls which made his stronger. He sought revenge upon Dagon and planned to use the Prince's invasion to seek it. He visited the shrines of each prince and obtained their artifacts and blessings under the guise of a mere mortal, further increasing his power.
Eventually the Usurper Camoran was slain but Dagon breached the walls of Nirn all the same. Cutting through Dagon's servants Khorne entered the Imperial City and came face-to-face with Dagon. But before Khorne could strike the dragonborn Martin Septim banished Dagon back to Oblivion with the aid of the Divine Akatosh. Khorne was left with no way to retain his true place as Daedric Prince...until Sheogorath opened his Realm to Nirn, looking for a champion.
Khorne aided the Madgod in his quest to halt the Greymarch and in return was made to replace him. Khorne's mortal body was warped over time to fit the Madgod's preferred appearance and mind. Khorne felt imprisoned in this form and sought an escape. After 200 years he had enough power built up to return to Oblivion, leaving the Breton vessel to become the pure Madgod. Once back in Oblivion he constructed a new vessel but this one was not born from mortal parents as the last was, it was made perfect for Khorne's purposes from the start and did not receive a soul of it's own.
Khorne possessed this Dunmer Skin immediately just as the Dragon Crisis had begun. Khorne set about to construct his own realm using the combined powers locked away beneath the surface of Skyrim, left by the ancient Dwemer. He once again obtained the artifacts and blessings of each prince (including Dagon) and used them amplify his power on Nirn. Being the Prince of Rebellion he aided the Stormcloaks in their civil war and brought destruction to their enemies. He even attempted to use the Eye of Magnus for his own gains but it was destroyed by the new Dragonborn. Khorne is currently fighting through Black Reach looking for remnants of the Deep Elves' power...

I have this one character named Bob who I recreate all the time in many different RPGs, including TES. Usually I just leave it at descendants.

Bob I

Bob V

Bob XXI

etc

But I also have a vampire Bosmer character (Valencia Ridd) that showed up in three games with the same personality (roughly), playstyle, and factions.

Otherwise I just create my characters game-by-game.

My character Hunter was suspended in a pocket dimension by an unknown force.

Sort of like Gordon Freeman and the Gman

Bilal is Immortal, well so long as he has the Ring of Hircine, he lost it during the Oblivion Crisis but found it shortly after. Then some idiot named stole the ring from Hircine who had stole from me who i had stole from the dead body of that Nord Chief in Solsthiem all those hundreds of years ago

Everything comes full circle eh?

My 1st skyrim guy was a fresh face but i did bring back my altmer mage from OB...it works because he's a altmer and magical so theres many ways he can still be alive. I also made him appear older in skyrim to keep up with appearances

When playing an Elf I make him old in Skyrim if he's a carry over.

Humans are usually just decendants of my Oblivion character.

I have never really played a character like that, I like the idea of the descendants that is a good way of doing the same character. None of my Characters In oblivion deserve to be remembered or even to live for the 200 years between games.

Oh also my Main guy is a Vamp who was the Listener in Oblivion but was buried alive (undead?) and only escaped after 200 years due to the Thalmor invasion. When he saw what the DB had become he butchered that [censored] astrid

Never yet made a character who I've RPed as being the same character or a descendent of a character in a different game
On the other hand some of my characters could've been clones of those I've played in previous games. I blame Divayth Fyr