Occasionally; if I really liked a character but the campaign they were in was short-lived and I didn't get to play them enough to be satisfied and explore them. If they died or I got to play them over an extended period and see what happened to them, no.
For example, I always liked the idea of the Half Ogre from the old Dragon magazine articles, and I loved the name "John Grond" given in one of them as one from the author's campaign. This past year I rolled a very high strength Fighter in an OD&D game online, and I decided that after 30-ish years I would finally play my own John Grond. While the DM didn't actually want to use rules for a half-ogre race, he was open to me describing John as close to 7' tall, massive, beetle-browed and hulking, with slightly too-protuberant and pointed teeth, etc. John is Chaotic, bold, crude but cunning, and revels in his size and power, happy to smash down doors and bellow at monsters. Sadly, that DM had to end his game shortly after I made John, and I only got to play him once or twice. So when another OD&D DM invited me to join his game, I asked if I could import John, and he was open. John's been running strong in the new game for several months, has made 4th level, had a number of excellent adventures and I'm still enjoying him quite a bit.
I also like the idea of using existing characters in a higher level one shot or limited adventure, like Conan appearing in a new short story. "Hey guys, we're finally going to try Tomb of Horrors; who wants to bust out your old high level characters?"