Minecraft 13w39b, Minecraft 13w48b, Minecraft 1.7.4, Minecraft 14w02b, Minecraft 14w02c, Minecraft 14w29b
Spiders only become faster when they have a speed potion effect or a raised "movementSpeed" attribute. Even when they should be extremely fast, they remain similar to a normal spider speed.
To recreate, put this command into a command block:
The spider summoned will not be much faster than a normal one. To prove that it should be, you can try the same command with a zombie instead of a spider, and you will see that it moves extremely fast:
UPDATE: This also doesn't work with Iron Golems, and I would guess many other mobs are not affected either.