Found this in a thread on reddit, but I won’t dare to assign a class.
- Fire and light manipulation: This is Gandalf's most commonly seen power - he is described as having "made a special study of bewitchments with fire and light", suggesting he is exceptionally talented in this area. His feats include emitting light from his staff, breaking the Bridge of Khazad-dûm using white light, dispelling the Nazgûl using white light, and killing multiple orcs with "a terrific flash like lightning". His staff seems to be important in performing this magic, and of course it's hotly debated whether his possession of the Ring of Fire was linked to his light and fire abilities.
- Telepathy: Gandalf can seemingly read Frodo's mind while he is asleep ("It has not been hard for me to read your mind and memory") and communicates with Elrond and Galadriel by thought alone. He is also able to tell that the One Ring is beyond his influence after reuniting with Aragorn's party.
- Telekinesis: Gandalf can move (and change the colour of) smoke rings without physically touching them. He also disarms Legolas, Gimli and Aragorn and breaks Saruman's staff.
- Blessing: Gandalf blesses both Bill the pony and Butterbur's beer. Bill subsequently escapes to Rivendell against the characters' expectations.
- Healing: Gandalf is able to heal Theoden, both spiritually and physically ("You do not know your own skill in healing").
- Transmogrification: Gandalf suggests he is capable of turning a hobbit into an animal ("And see that Sam Gamgee does not talk. If he does, I really shall turn him into a toad"). There's no hard evidence that Gandalf was joking when he said this, and in fact I'd argue it would be out of character for him to joke about things he was entirely incapable of doing.
- Opening and closing spells: Gandalf uses "various incantations" in an unsuccessful attempt to open the trolls' cave. At the Doors of Durin, he mentions knowing over 200 spells for opening doors. Later, at the Chamber of Mazarbul, he refers to knowing "many" shutting spells.
- Word of Command: Gandalf speaks a word of Command to counter the Balrog's counter-spell. The context suggests that this is a means of making his own spell stronger.
- Compulsion: Gandalf is able to force Saruman to look at him against his will using only his voice.
- Creation of magical items: Gandalf gifts the Old Took "a pair of magic diamond studs that fastened themselves and never came undone until ordered" (although it's possible these were made by someone else). His fireworks could also be interpreted as being magical.
Inspiration - Gandalf brings hope to people. The White Rider counters the effects of the fear from the Nazgul, for instance, and his talk to Theoden helps bring him back from the despair he has sunk into. We are told in the Silmarillion that he often does this in secret, putting fair thoughts into elves' heads without them knowing the source.
Insight - He has a particularly strong gift for seeing the way things should be. He knows, somehow, that calling on a mere hobbit to join 13 dwarves would lead to some unnatural good. He knows that Merry and Pippin would serve a strong purpose in joining the Fellowship. He knows that Bilbo did right to show Gollum mercy. He knows there is something wrong with the ring Bilbo finds...
Pity - For a powerful being Gandalf shows an exceptional amount of pity and care for all those who dwell in Middle-Earth. He travels all lands, he communes with those high and low, and he knows details of the most little things. Not because he seeks knowledge, like Saruman, but because he really cares about all these things. And in the end this gives him a power to move the world for good.
