Which is the fastest class in WoW?
First I'll go through speeds without mounts (assuming you're inside - which excludes druids travel form):
Fastest passive on Foot
Hunter - they have access to Aspect of the Cheetah and Glyph of Pathfinding, which increases movement speed by 38%.
Fastest speed on foot when using activated abilities
Rogue - Stealthed rogue with the bonus is 131% (which is slower than the hunter), but you can use Burst of Speed infinitely which will bring it up to 204%.. in addition they can occasionally use sprint which is a temporary speed boost that totals at 220%.
Runner up - Paladin - with the correct talent and always having 3+ holy power, they can run fast as well.
Now let's talk about mount speed.
Death Knights and Paladins are tied when on mounts. I'll talk about flying mounts for the sake of numbers.
Death Knights have access to Pale Horse, and Paladins have access to Crusader.. if you have those with the fastest possible flying mount skill and the fastest type of mount (310%), and have the guild perk which increases mount speed, you can get up to a total of 392%.
As for stacking movement effects.. not many effects stack with each other as of Cataclysm/MoP. Some examples:
Carrot on a Stick will indeed increase your movement speed, but it does not stack with effects such as Crusader. Therefore, once you get crusader, the movement speed bonus from Carrot on a Stick becomes useless.
Mithril Spurs also becomes obsolete when you get the guild perk "Mount Up". The same goes for Riding Crop and the Riding Skill enchant.
In conclusion, the fastest mounted classes are Paladins and Death Knights, while the fastest class on foot is the Rogue.