All the previous answers are very good but let's sum this up. The actual examples of his actively working power are:
-ability to conjure and control fire (including heating up objects and igniting them at distance), light (of varying intensity), smoke (glowing in many colours, scattering white sparks)
-control over water as seen in the flood wave of Bruinen
-moving objects with mind (telekinesis) by using staff or gesture (,,But Gandalf sprang up the steps, and the men fell back from him and covered their eyes; for his coming was like the incoming of a white light into a dark place, and he came with great anger. He lifted up his hand, and in the very stroke, the sword of Denethor flew up and left his grasp and fell behind him in the shadows of the house; and Denethor stepped backward before Gandalf as one amazed.")
-spells and blessings (shutting spell on the door of Mazarbul chamber and opening ones at the west gate of Moria, ,,words of guard and guiding" at Bill the pony, blessing on Butterbur's beer, Word of Command which seems like some special show of power to control material objects: ,,Then something came into the chamber- I felt it through the door, and the orcs themselves were afraid and fell silent. It laid hold of the iron ring, and then it perceived me and my spell. What it was I cannot guess, but I have never felt such a challenge. The counter-spell was terrible. It nearly broke me. For an instant the door left my control and began to open! I had to speak a word of Command. That proved too great a strain. The door burst in pieces.")
-explosive blasts capable of tearing up stone structure (,,At that moment Gandalf lifted his staff, and crying aloud he smote the bridge before him. The staff broke asunder and fell from his hand. A blinding sheet of white flame sprang up. The bridge cracked. Right at the Balrog's feet it broke, and the stone upon which it stood crashed into the gulf, while the rest remained, poised, quivering like a tongue of rock thrust out into emptiness."
,,The tower behind was crumbled into dust, the window gone; the ruined stair was choked with burned and broken stone”’)
-lightning flash that kills instantly several goblins (,,But not Gandalf. Bilbo’s yell had done that much good. It had wakened him up wide in a splintered second, and when the goblins came to grab him, there was a terrific flash like lightning in the cave, a smell like gunpowder, and several of them fell dead.")
-,,white fire" the stream of light which drove out Nazgul (,,Like thunder they broke upon the enemy on either flank of the retreat; but one rider outran them all, swift as the wind in the grass: Shadowfax bore him, shining, unveiled once more, a light starting from his upraised hand.
The Nazgûl screeched and swept away, for their Captain was not yet come to challenge the white fire of his foe…")
-mental powers (,,you talked long in your sleep and it was not hard for me to read your mind and memory", communication of thoughts, inducing fear or strengthening courage, likely by the power of ring, mentally fighting the will of Sauron ,,I sat in the high place and strove with Dark Tower" trying to free Frodo's mind from Sauron's influence at Amon Hen, he was the voice that urged the hobbit to take off the ring, putting ,,fair visions and promptings of wisdom into the hearts of elves")
-unusual endurance, strength of body and speed (physically fighting with Balrog which is ,,stronger than a strangling snake", acting in ,,splintered second", ,,nimbly as a goat", ,,the old man was too quick for him", ,,Gandalf revealed the strength in him" while easily lifting Faramir's body, keen senses: ,,One sign of the change that he soon noticed was that he could see more in the dark than any of his companions, save perhaps Gandalf.")
The physical traits might be magical because his power comes from the spirit and the stronger the spirit is the more control over body it can exert (like in case of elves, their spirits have greater control over body than it is among Men).
The one of his abilities is probably also to make illusions to appear tall and menacing and move unseen, prevent from recognising his identity: ,,Gandalf! What veil was over my sight", use force of mind to paralyze people/or command them: ,,Gimli started and then stood still like stone staring...", ,,the others relaxed and stirred as if a spell had been removed", ,,Legolas bent bow slowly as if some other will resisted him", ,,'Come back, Saruman!' said Gandalf in a commanding voice. To the amazement of the others, Saruman turned again, and as if dragged against his will, he came slowly back to the iron rail, leaning on it, breathing hard. His face was lined and shrunken. His hand clutched his heavy black staff like a claw."
All this examples were performed in carefully chosen moments, usually Gandalf tries to restrain himself from using his abilities so to not assume direct control over others through such disaplys of power and instead inspire the inhabitants of Middle Earth to work things out for themselves, lending only his knowledge and wisdom through subtle advice.