I've played DnD since 3.5, and am well aware of how they all implemented Psionics, but feel I need a better look outside of the DnD world.
So I'm curious about the wider range of RPGs. Which systems have had good implementations of Psionics, and what made them good for you? I'm especially interested in RPGs that had Psionics existing alongside other Magic systems, but in general, what makes for a good Psionics system?
Traveller has the same five core powers in all editions: telepathy, teleportation, telekinesis, teleperception (aka Clairvoyance), and Awareness (which is attribute buffs, and similar to the prana bindu from Dune). Various editions have a variety of others, including unaging, postcognition, and machine telepathy.
Implementation varies wildly by edition.
It's worth noting that the core 5 abilities are pretty much straight out of Lensman.
Palladium has essentially 3 magic systems across its lines...
There are some that use a semi-vancian slots-per-day, not unlike 5E, but 30 years earlier. Spells of Level X require level X in the relevant class.
There are some that use Magic Points, otherwise similiar to semi-vancian, must be Level X to cast spells of Level X
Psionics differ - they can be present in almost any class, are rolled for randomly, and while they have spell-like descriptions and cost ISP, but you do not need to be in a specific class to have them. Minor limits to level 1 psionic powers only, major to level 1-3, master to 1-10. Which specific ones are random - at level one, roll for each psionic power of the new level...
Note that Palladium Fantasy also has a system of magic circles for the summoner, and of runes... each class linked.
Rolemaster/Spacemaster: Psionics are just a 4th school of magic (the other three: Esssence, Channeling, Mentalism). They all work near identically (differing mostly in armor penalties), but the spell lists are class-linked, and expensive for further afield lists than one's class' core & closed lists. They all cost SP equal to the spell level, and no casting check if under character level and level to which list is known, and obeying restrictions; attack spells always require an attack roll, separate from the casting check...
Tunnels and Trolls and The Fantasy Trip both have all magic being psionic; there is no distinction betwixt them
GURPS has magic separate rules from Psionics, but Superpowers and Psionics are the same rules. All require skill rolls, but differ in acquisition and progression .
Savage Worlds. in core, the differences between flavors of paranormal abilities determine how obtained, and which powers can be obtained. Core includes Faith, Mage/Wizard spells, Weird Science, Psionics, and Super powers. Additional flavors get added in some worldbooks... Deadlands adding Tribal Shamanism, and Martial Arts mastery.