Minecraft – Despawning monster mobs

My answer is no longer correct, even though, at the time of posting, it was. Look to some of the other answers (particularly the bounty winner) for more up to date information.

Most important rule: when a chunk is unloaded, so are the mobs (and all other items) on it, although passive mobs won't be removed.

There is also a limit on the number of mobs that can be loaded at one time: 200 hostile and 15 neutral mobs (I don't know if there's a limit on passive mobs). Also, hostile mobs are removed if they leave the 9x9 chunks that they're allowed to spawn in.

Running away will usually allow you to stay out of the reach of hostile mobs, since a chunk needs to be loaded a certain amount of time before mobs will start to spawn, but the chunks immediately behind you could have the max allowable mobs, making it dangerous at best to turn around.

Take a look at the wiki for more information.

Based on your comment:

In a straight line, not in water, you can out run every creature save for an angered enderman simply because its teleportation is sporadic. Where you might get into trouble is when the terrain is not easy navigated and you have to jump and hop. The AI will always do this perfectly, and while it does slow them down a bit its not as much as if you miss your jump and have to do it again as this will often cease your forward motion.

If you are Sprinting (you double tapped) you will very easily outrun everything. Even a teleporting enderman will have a bit of a task to keep up with your movement.

On a difficulty scale for out running creatures it goes

• Zombie
• Slime (And Nether version)
• Creeper
• Skeleton and Nether version (Flame guys, embers?)
• Spider
• Enderman
• Ghast
• Zombie Pigmen (which are faster than your run)

16 blocks is the active range for AI with two notable exceptions. Zombies and Slimes are all 'touch' based and so the easiest to keep out of range and get beyond that 16 block range unscathed. Creepers are next because of their AOE for exploding gives them a bit of an advantage over the 'touch' range. Skeletons can shoot their arrows pretty far making them a bit more tricky, but honestly if you keep moving they generally keep missing. Spiders might just be my pet peeve against them but they have a ground speed that is higher than most other creatures and are able to scale vertical heights with out as much difficulty as the other mobs (though its still the best way to lose them if you can jump reliably). Endermen are in the annoying category. They have a high range of activity to them due to their ability to teleport. However, constant motion does seem good enough to keep them from doing too much to you. Last are the ghasts simply because of their huge range, around 96 blocks if I recall correctly. They are not limited to path finding and just need a line of sight to constantly launch balls of fire at you.

Anywho, I know this isnt exact numbers for their speed vs your character's speed but this is a very observable measurement with out having to get into the exact numbers in that manner so I figured a through explanation might suffice.

Hope this helps.