Yes, I use psionics. In my current game, it would fall somewhere in the "Yes, but limited by race/location, etc" category.
Breaks down something like this: magic, as it's traditionally understood, is the harnessing and shaping of an ambient, natural power - mana - the presence of which is a function of defined existance. It's here because it being here is written into the set of principles that define what 'here' is. 'Here' being the entirety of the multiverse.
But there is a place that isn't here. The difiniatory not-here that makes up the Far Realm. Seas of roiling chaotic madness where impossible possibilities overlap and comingle, each equally valid, each equally real. In the deeps off these far shores titanic intellects swim, dreaming horror. Mana is a function of defined existance, and defined existance is antithetical to where they call home, so in the absence of an external power by which to fuel the hand of their will, they turn instead turn inward, drawing from themselves. From this is birthed psionics.
My current game takes place in a modified version of the Forgotten Realms. In this version, psionics are the sole perview of these Outer Gods and their childer races - illithids, aboleths, yuan ti, etc, and their presence on Faerun is very faint. In these Realms right now, the only way a normal person would have psionics would be if they had been experimented upon by one of these races. On other worlds where the presence of these beings is much more pervasive (Eberron, for example) the knowledge and practice of these internal arts has filtered down through the populace to the point where it's possible for normal people to manifest psionics.
So right now in my game, psionics are present, but arn't available as a PC option. They're wierd, alien, mysterious things that the bad guys do that make no sense and fly in the face of the understood rules that govern magic. Later on, however, as events progress the psionic option may (and likely will) open up to developement.