Over time, you can perm all the skills obtainable, one at a time. There is no limit. (of course, you can still run out of skills, since there are a finite number of them, but that's another issue altogether)
However, something that the wiki doesn't make clear (although, makes sense once you get there) is that each skill has two "levels" of permanency. A skill can be hardcore or softcore permanent, depending on the type of run you just left (your first run counts as softcore). If it's SCP (softcore permanent), then you keep it for all softcore runs, but not for hardcore runs. On the other hand, if you make it HCP (hardcore *), then you keep it for all runs, including softcore.
(But, not Bad Moon, which is another topic altogether)