How do I make an enderdragon in a minecart face west instead of north?
The Rotation NBT tag must be edited to change this:
/summon ender_dragon ~ ~ ~ {Rotation:[yRot,xRot],NoAI:1}
In your case:
/summon ender_dragon ~ ~ ~ {Rotation:[0f,270f],NoAI:1}
This command will summon a dragon facing straight west. Other increments of 90 will give one of the remaining cardinal directions. Changing yRot changes the up/down angle.
If you already have a spawned Ender dragon, you can edit its NBT by the entitydata command:
/entitydata @e[type=ender_dragon,limit=1,sort=nearest] {Rotation:[0f,270f]}