I've got a foot in either end of the spectrum.

I reuse characters in fandom settings if I feel they didn't get a good run because of a game's early death, I still have a story I want to tell with them, or it's a series/ sequel. Like Harbinger said, it feels like a waste of time and energy if you spend days researching and creating a character only for it to get snuffed out in a few weeks because a game died. If a character is adapted to the new RP and setting, I don't see the problem.

On the other hand, there's something stagnant about reusing the same character across different genres and games and it brings to mind Theseus' Ship; if you replace every plank of wood on a ship across it's life, is it still the original ship? I had a conversation with a good friend of mine about her habit of reusing characters but basically changing everything but the appearance and name... if a character is so vastly different between incarnations, aren't you technically playing a different character? 

Personally, I get bursts if inspiration for different ideas so while I have a handful of repeat characters, I write and create so many more original ones because it makes sense for different games. It's all very circumstantial.

Where I take exception and issue with people reusing characters is when it's an obvious author insert and/ or it's the same character across different RPs with no changes to accomodate the new setting. I've seen it a few times on the guild and it's definitely enough to make me steer clear. You need to respect a GM's setting and lore and make your character work for it, not awkwardly cram in a failed post apocalyptic setting character into a fantasy RP and then into a slice of life romance and then into a scifi setting with virtually nothing changed.