Some examples I've read (which no one else has mentioned yet) in urban and YA fantasy include:
- Talents
- Sparks (used in the Girl Genius comics)
- Graced (Graceling novel series by Kristen Cashore)
- Mages (generic, but it still works even in modern and futuristic settings. There are also many variants on mages, like 'magids', 'mancers', and so on.)
- Mutants (X-Men)
- Workers (as in magic workers, from the Black Cat series by Holly Black)
I know I've seen many other original names, but I can't remember them off the top of my head. Some stories use more generic but nuanced terms like witches, wizards, magicians, espers, and so on, even for characters with wildly varying powers.