There have been versions of psi (though not unlimited breadth; psi's with broad-band abilities are actually pretty rare in fiction once you get outside of superheroes), but, well, it tends to overfavor the lucky and intimidate those that aren't.
Not really, at least not in mainstream accessible Sci-fi/Space Opera...
Let's see... Traveller and D&D provide the classic abilities in gaming: Teleportation, Telekinesis, Telepathy, telepathic violence, teleperception (life sense, remote viewing aka clairvoyance, remote listening/clairaudience), short term mind control, the ability to heal oneself, the ability to heal others. One that neither routinely includes, but which mainstream sci-fi does, is matter transmutation.
Let's examine a few universes...
Star Wars: Telepathy (ESB), Mind Control (ANH), Teleperception (ESB, RotJ), Speak with Dead (ESB, ANH), transform into Force Ghost (done in ANH proven by RotJ). Telekinesis (ESB), Precognition (ANH, ESB). We even get "force lightning" in RotJ. The one thing we really don't see is Teleportation, except maybe in RoS, tho that might instead be Luke as force ghost or luke using Telepresence. Unclear, the canon is, unclear.
Star Trek: S1E2 Charlie X... Telepathy (super strongly implied, teleperception (implied), mind control, matter reorganization (Perfume, de-facing a sciences gal, transforming Yeoman Lawton into an iguana), thermokinesis (melting the chesspieces), matter deletion (may simply be reorganizing into air - the phasers, a couple people.) Telepresence (Thasian manifesting as glowing face).
The Cage: telepathy. Loads and loads of it.
The Man Trap: salt extraction. No, I'm not joking.
Where No Man Has Gone Before: Telekinesis and Teleperception. A bit of matter destruction. (Instant grave.)
The one we don't see? Teleportation... well, actually, we do. In Picard, season 2. Wesley Crusher. He also can time travel, apparently. The TNG episode
The Traveller implies warp manipulation.
Barbarella - The Angel flies; the intent may or may not have been autotelekinesis (a fancy word for flight by telekinetic means), but given the almost laughable lack of use of his wings, it looks onscreen like autotelekinesis.
Original BSG: I honestly can't think of any other than Count Iblis' abilities, but he's (literally) the devil.
Babylon 5: Lots of telepathy. Very limited teleperception, a little bit of telekinesis (Soul Hunter). Transcendence to angelic form (Vorlons, Elders). Autotelekinesis (Kosh).
Orson Scott Card's
Enderverse: The Ansible network and the Bugger Queen both are telepathic (it's even FTL). Near the end of the cycle, we also see FTL long range teleportation.
Lois Bujold's
Vorkosiverse: there are some very mild implications towards precog and telepathy, but nothing concrete... but only a few have the mind to manage a jump... and they require a neural interface implant to control the machine. And a human mind is an absolute requirement.
Anne McCaffrey's
Federal Teleport and Telepath setting: we see exoteleport, telekinesis, limited telepathy, limited precognition. Exoteleport becomes even FTL. It's worth nothing that the telepathy is very limited; this is unusual in a clearly psionic setting. Novels include
To Ride Pegasus,
Pegasus In Flight, Pegasus in Space, The Rowan, Damia, and more.)
Anne McCaffrey's
Pern: Telepathy, but not human-to-human, only Human to/from dragon, and dragon to dragon. Dragons can also teleport. And can do so across time. There are some implied clairvoyant/precog aspects of a couple characters, too... most notably Lessa. Note: it's a Sci-Fi setting, despite the appearance of being Fantasy. This becomes very clear in certain later volumes.
Cole & Bunch's
Sten series: One of the team is telepathic.
Robotech: The Invid have limited telepathy, and certain ones limited clairvoyance. The Palladium version of the RPG only give telepathic communication as if speech. (Robotech RPG Book 5,
Invid Invasion, Page 75). The Robotech Masters have projective telepathy, flight, limited telekinesis, read emotions, and danger sense. Their eidetic recall is, in RPG terms, treated as a psionic ability; in the show and novels, it's not noted as such, and probably isn't, but since eidesis is a psionic ability in other palladium games....
Doc Smith's
Lensman: We have telepathy and teleperception near universal to Lensmen. Certain Lensmen have more..
Buck Rogers TV show. We see telepathy, telekinesis, clairvoyance. (The episode guest starring Jack Palance).
That's not "rare"... Psionic abilities are a staple of Space Opera. Sometimes augmented with technology.