Anyone is welcome to add to this list; just make sure to include a verifiable source. I used mainly the E3 gameplay videos for this list.

Alteration
Detect Life

Restoration
Circle of Protection
Healing

Illusion
Clairvoyance
Frenzy

Destruction
Chain Lightning
Fire Breath
Flames
Frost Rune
Frost Bite
Fireball
Firestorm

Conjuration
Frost Atronach

Specific Spell Descriptions:
Chain Lightning-Bolt of Lightning that does 50 points of damage and twice as much Magicka damage, then leaps to a new target. Level Adept Cost 45
Fire Storm- A 75 point fiery explosion centered on the caster. Does more damage to closer targets. Level Master Cost 148
Fireball- A fiery explosion for 75 poitns of damage in a 15 foot radius. Targets on fire take extra daamge. Level Adept Cost 57
Flames- A gout of fire that does 6 points of damage per second. Targets on fire take extra damage. Level Novice Cost 5 per second.

What I found extremely interesting is that each of the above listed Destruction spells seemed to have levels of their own despite the player have 80+ Destruction skill which begs the question, what determines spell level if it's not skill level?

In all likelyhood since spells now function very similarly to weapons in terms of having to equip them there is also a system in place where you have to buy and find more powerful versions of spells to create some equivalence on that end.
In all the previous Elderscrolls games looting dungeons was never really that exciting for mages because you couldn't find any rare and powerful spells like you could weapons and armor.

Fire breath is a shout, not a spell, isn't it?

And paralyse is confirmed to be in Alteration.