I was actually intrigued enough by this... and bored enough... to do a search for all the various spells he's cast. I tried to eliminate repeats as much as possible, although some of the banishing spells are just too funny to leave out (Banish: Time-Traveling Vikings - who spends their afternoons creating that spell?) I gave up on repeating the incantations, unless I found them funny or interesting... we usually think of him a a good guy... but get a load of the demon summoning stuff!
Bottom Line:

Don't mess with the Doctor!
Usual Equipment
Orb of Agamatto
A globe used to monitor outbreaks of evil magic around the world and the heavens, and in parallel dimensions. Contains its own "unreal, subjective" universe.
The Eye of Agamotto
Strange uses this to see through illusions or other distortions of reality, hidden individuals (whether invisibile, astral, or otherwise) and use mind magick such as telepathy, or to examine the mystical auras of individuals. Postcognition, Precognition. Analyzes magical phenomena. Sometimes used to diagnose ailments of the soul.
The Cloak of Levitation
Provides flight and levitation abilities to the wearer, can also be used to manipulate objects and grapple. Controlled by his willpower.
Ring of the Ancient One
Allows Strange to assume the appearance of his predecessor, the Ancient One. May possess other powers, such as storing spells or rituals for later, instant release.
Various wands, staves, orbs, artifacts and other items of power stored in his Sanctum.
Common Technique: Astral Travel, unlimited range, dimensional travel via astral form.
Common Spells:
Banish: Forces of Darkness
I summon the powers of the Vishanti!
By the spell of the Dread Dormammu,
in the name of the All-Seeing Agamotto --
all thy powers I summon ---
begone, Forces of Darkness!
Conjure: Evil Power of Dormammu
Dormammu accept my incense offering!
Let the force of your power descend upon
my enemy! Let him feel your fatal touch!
I beseech you, Dormammu!
Conjure: the Mists of Hoggoth & the Path of Hoggoth
which leads to Nightmare's world
Invoke: Forces of Good
By the power of the Vishanti --
in the name of the All-Seeing Ancient One --
I summon all the forces of good --
and focus their blinding power upon you,
through the facets of this ring!
[Note: this must be used in conjunction with a ring.]
Conjure: a Strange Tale (Basically, summon plot exposition)
Let the flames thus flicker low,
let the silent shadows steal,
let the lonely candles' glow
our mystic tale -- reveal!!
Space: Dimensional Travel Portal ;
Banish: Eerie Imprisoning Mists ;
Banish: a Being to its Home Dimension
Repulse: Humans, 5' (or larger) Radius
I summon the spells
of the omnipotent Oshtur!
Banish: Beings From Whence They Came ;
Banish: Being From Whence it Came ;
Conjure: a Giant Hand from a Shadowy Dimension ;
Time: Distortion (A Rhymed Incantation, ie: )
Hammer of Thor, return to your master!
Though he was falling, you fall faster!
Time: Travel to the Past ;
Banish: Darkness ;
Banish: Someone to the Time of their Origin ;
Space: Dimensional Travel ;
Banish: All-Purpose;
Misc: Strengthen Another;
Control: Paralyze Another ;
Control: To Teleport Another;
Conjure:Bands of Cyttorak (Reveal and ensnare hidden or unseen foes, general ensnarement) ;
Banish: Bands of Cyttorak;
Conjure: Orb (called "Eye") of Agamotto;
Banish: Mind-Clouding Spell
By the vapors of Valtorr, let thy mind be cleared!
Banish: Vapors of Valtorr; Banish: Entrapping Spell; Conjure: Cloak or Amulet; Banish: Evil Spells of Entrapment and Exile; Conjure: Shades of the Shadow Demons; Control: Paralyze and Brainwash; Banish: Mystic Bonds; Banish: Various specific beings and demons; Conjure: Visions of the Past; Conjure: Twin Spirits; Control: The Mindless Ones; Banish: Control Over Others ; Banish: an Enchanted Prison; Space: Rapid Dimensional Travel; Banish: an Evil Spell; Banish: Self ; Misc.: an Oath of Vengeance ; The Mystic Maze of Madness; Banish: the Mystic Maze of Madness; Space: Levitation Without a Cloak; Space: Teleportation; Conjure: Rings of Raggadorr; Misc.: Restore Cloak; Conjure: a Vision; Conjure: a Sign Leading to the Source of Evil; Control: "The Spell of Exorcism"; Control: Transferral of Powers (steals powers and places them into an orb); Conjure: Black Lightning; Control: Attract Attention; Misc.: Open Doors; Misc.: Destruction of Threatening Things (Machines); Conjure: Flaming Whip; Conjure: Darkness; Conjure: Vapors of Valtorr (two minds required... vapors do mind-meld); Misc.: Using the Cloak of Levitation as a Weapon; Conjure: Light; Banish: Subjective Vikings (
); Banish: Vertigo (Restore balance); Banish: Young Women to Earth-M (
); Conjure: the Herald of Satannish; Conjure: Cloud Concealment; Banish: To Stop Someone From Levitating or Flying (Go splat!); Control: Awaken Another From a Mystic Trance
Misc.: "The Trance of Transferral"
By the dark that hides the day --
by the misbegotten word
to one whom we obey --
our powers be now -- transferred!
Conjure: Ymir and Surtur (Yikes!); Banish: Party-Goers (
); Conjure: Crystalline Imprisonment; Control: To Teleport Demons
Banish:Webslingers (I sh!# you not.)
Demons of darkness!
In the name of Satannish!
By the Flames of the Faltine
Let Spiderman vanish!
Conjure: Illusion of One's Body; Banish: False Appearances; Space: Teleportation to Earth; Control: Stop a Truck; Conjure: Tiling a House; Control: Brainwash; Control: To Clear a Hypnotised Mind; Banish: "Living Wickedness" From Furniture (????); Conjure: Illusion of Normality (probably needed after that last spell); Misc.: To Cease Dying (!); Misc.: Spell Against Death Which Was "Not Permitted" (

); Control: Another's Mind; Conjure: The Circle of Cyttorak; Conjure: Mists of Morpheus (Magic knock-out gas); Control: Banish Another's Consciousness (

); Conjure: an Awning to Cushion Someone's Fall; Conjure: Winds; Conjure: Shield of the Seraphim; Conjure: Power (

); Banish: Falsehood; Transmute Guns to Snakes; Conjure: Hurricane (

); Conjure: Octopus (

);
Control: to Reverse the Foregoing Spell
Let all be as it once was! (Whew!)
Control: Psychoprophylaxis; Conjure: Light and Guidance; Banish: Despair Through Light;
Banish: a Villain into a Pocket-Dimension; Conjure: a Triple Shield of Protection; Banish: an Evil Bird (
); Conjure Nightmare; Conjure: Faltine Flames; Misc.: Reassemble Broken Statue; Conjure: Gaping Abyss (
); Transfer: Forms (Hey, babe! Let's swap bodies!); Banish: Weapon's Power; Release: Captive; Banish: Weapon; Control: Sap Another's Strength; Misc.: Strengthen Another
Rituals: Depending on resources (books, material components, time) he can simulate just about any power by performing a ritual of varying length and complexity.