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:
/summon Spider ~ ~2 ~ {ActiveEffects:[{Amplifier:80,Id:1,Duration:199999980}],Attributes:[{Name:generic.movementSpeed,Base:3000.0}]}
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:
/summon Zombie ~ ~2 ~ {ActiveEffects:[{Amplifier:80,Id:1,Duration:199999980}],Attributes:[{Name:generic.movementSpeed,Base:3000.0}]}
UPDATE: This also doesn't work with Iron Golems, and I would guess many other mobs are not affected either.
Related issues
is duplicated by
Comments


Is this still a concern in the latest Minecraft version 13w48b? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.

Confirmed for 1.7.4
EDIT:
List of mobs the movementSpeed works with and doesn't work with:
Command used for all of the mobs listed below:
/summon Creeper ~ ~1 ~ {
Attributes:[
{
Name:generic.movementSpeed,
Base:5
}
]
}
movementSpeed DOES work with:
1. Creeper
2. Skeleton
3. Zombie
4. Witch
5. Pig
6. Sheep
7. Cow
8. Chicken
9. Wolf
10. MushroomCow (Mooshroom)
11. Ozelot (Ocelot)
12. EntityHorse (Horse)
13. Villager
14. VillagerGolem (Iron Golem, also contrary to the report, this does work)
15. SnowMan (Snow Golem)
16. WitherBoss (Wither)
movementSpeed does NOT work with:
1. Spider2. PigZombie (Zombie Pigman)3. CaveSpider4. Silverfish
5. Giant (seemingly not a supported mob anyway)
6. Slime (intended: it jumps to move)
7. Ghast (intended: it flies to move)
8. LavaSlime (Magma Cube, intended: it jumps to move)
9. Bat (intended: it flies to move)
10. Squid (intended: it swims to move)
11. EnderDragon (intended: it flies to move)
movementSpeed behaves strangely with:
1. Enderman (its speed is increased but seems to hit a max, moving much slower than other tested mobs but still faster than normal)2. Blaze (same result as Enderman)
List of mobs the "Speed" potion effect works with and doesn't work with:
Command used for all of the mobs listed below:
/summon Creeper ~ ~1 ~ {
ActiveEffects:[
{
Id:1,
Amplifier:50,
Duration:1000000
}
]
}
The "Speed" effect DOES work with:
None
The "Speed" effect does NOT work with:
All

Confirmed for 14w02c

The "movementSpeed" attribute has been fixed for all applicable mobs. The Speed and Slowness potion effects still do not work but only when applied through dataTags in the /summon command. The /effect command will work, though. No idea what that's about.
A bug report specifically concerning the Speed and Slowness effects can be found here: MC-32575

Can confirm the list of Skylinerw for 14w29b please update discription
Also please add a "relates to" link to MC-32575 like Skylinerw said, as it could have the same reason

This has been fixed in 14w06a when these mobs got an AI update. Testes with all ground mobs (Spider, enderman, cave spider, silverfish, zombie pigman, blaze) that got the AI update. Please update the Resolution.
It seems like many attributes don't work for many mobs. followRange doesn't work for Giants for exemple