As a community we have been known to extrapolate greatly from the information that we are provided. So let's see if we can figure out the placement of the perks within their trees. I'm sure we can at least come close to the trees in the game. Keep in mind that the perks are not necessarily listed in order.

Credit goes to Sammuthegreat for most of these perk lists.

http://img580.imageshack.us/img580/9885/conjuration.jpg
- Novice for 50% magicka etc (up to Master)
- Dual casting overcharges --> greater spell effect
- Bound weapons do more damage
- Bound weapons cast Soul Trap on target
- Bound weapons banish certain creatures (and I think summon creature in their place, not 100% on that though, dodgy recording)
- Reanimate undead with 100 more health
- Summon 2 Atronachs or reanimated zombies
- Summon Atronachs at twice the distance
- Summoned Atronachs twice as strong

http://img600.imageshack.us/img600/1341/destructionp.jpg
- More damage for each school (fire, frost and shock) - ranked
- Novice for 50% magicka etc.
- Shock damage chance to disintegrate targets if their health is under 10%
- Frost damage chance to paralyse targets if health low
- Fire damage chance to make low health enemies flee
- Place runes 5x farther away

http://img231.imageshack.us/img231/7581/restorationh.jpg
- Healing spells also restore stamina
- Novice for 50% less magicka etc
- Healing spells do 50% more healing
- Something about recharging healing spells (sorry about poor recording quality, it was in my pocket!)
- More is recharged with each hit with healing spells (again, sorry not 100% sure what this means!)
- Spells more effective against undead
- Once a day chance to autocast 250HP restoration when health drops low
- Magicka regenerates 25% faster

http://img832.imageshack.us/img832/3642/alteration.jpg
- Novice for 50% less etc
- Alteration spells have greater duration (probably ranked)
- Absorb 30% magicka that hits you
- Another couple - bad recording again

http://img801.imageshack.us/img801/4042/enchantingo.jpg
- Enchants are 20% stronger (ranked)
- Enchanted armour 25% stronger
- "Soul gems provide extra magicka for recharging" - again, dodgy recording but that's what I heard, even if it doesn't make much sense
- Death blows to creatures but not people trap souls for weapon recharge
- Health, magicka and stamina enchants stronger
- Extra effect on already-enchanted weapon can be applied
- Shock, Frost and Fire enchants 25% stronger (individual perks for each element) (probably ranked)

http://img546.imageshack.us/img546/6325/heavyarmor.jpg
- Increase armour rating 20% (5 ranks)
- Unarmed attacks with heavy armour gauntlets - damage increased by gauntlets' armour rating
- Half fall damage if all in heavy armour
- Heavy armour weighs nothing and doesn't slow you at all
- Additional 25% armour if in matching set
- 25% armour bonus if all in heavy armour (not necessarily matching)
- 50% less stagger if all in heavy armour
- 10% damage reflected back to enemy if all in heavy armour

http://img268.imageshack.us/img268/8167/twohanded.jpg
- 2h weapons do 20% more damage (5 ranks)
- Attacks with warhammers ignore 25% armour (ranked)
- Attacks with battleaxes do extra bleeding damage (ranked)
- Attacks with greatswords do extra critical damage (ranked)
- Power attacks cost 25% less stamina
- Standing power attacks do 25% bonus damage, chance to decapitate
- Sprinting power attacks do double (critical) damage
- Sideways power attacks hit all targets
- Backwards power attacks have 25% chance of paralysis

http://img29.imageshack.us/img29/3623/smithing.jpg
- Steel Smithing: Create Steel armor and weapons at forges. Improve by double.
- Arcane Blacksmith: Improve magical weapons and armor.
- Dwarven Smithing: Create Dwarven armor and weapons at forges. Improve by double.
- Elven Smithing: Create Elven armor and weapons at forges. Improve by double.
- Orcish Smithing: Create Orcish armor and weapons at forges. Improve by double.
- Advanced Armors: Create scaled and plate armor at forges. Improve by double.
- Glass Smithing: Create glass armor and weapons at forges. Improve by double.
- Daedric Smithing: Create Daedric armor and weapons at forges. Improve by double.
-Ebony Smithing: Create Ebony armor and weapons at forges. Improve by double.
- Dragon Smithing: Create Dragon armor and weapons at forges. Improve by double.

All pictures are screenshots taken from official videos, so should be fine.

I think it was said by Sam that the Duel Casting was the first in the trees that didn't automatically have it.

Most amazing perks ever. Thank you Beth. You guys outdid yourselves. :tes:

Working on http://img580.imageshack.us/img580/9885/conjuration.jpg now.

Assuming that branches relate similar perks, I've split the perks thusly:

Bound weapons:
- Bound weapons do more damage
- Bound weapons cast Soul Trap on target
- Bound weapons banish certain creatures

Summons:
- Reanimate undead with 100 more health
- Summon 2 Atronachs or reanimated zombies
- Summon Atronachs at twice the distance
- Summoned Atronachs twice as strong

Magicka:
- 50% magicka reduction for Novice spells
- 50% magicka reduction for Apprentice spells
- 50% magicka reduction for Journeyman spells
- 50% magicka reduction for Expert spells
- 50% magicka reduction for Master spells

Should be first perk according to Sammu
- Dual casting overcharges --> greater spell effect

There appear to be 4 paths from the middle, so I need to think on this more.

Edit:
My guess is that bound weapon perks go on the left side (which has 3 perks, the other branches have more), in the following order bottom to top:
- Bound weapons do more damage
- Bound weapons cast Soul Trap on target
- Bound weapons banish certain creatures

Edit 2:
I want to believe that the right side plus the first one are the magicka reduction perks, simply because this would make a total of 5. However Sammu says that the dual wield perk is the first in the trees that have them, so I don't know if this is a valid guess. In this case the first perk up column 2 could be the dual wield perk.