Update 2 (2014-09-24): There is now a "grace period" of 5 minutes on all passive animal caps, and 1 minute on the hostile mob cap. This means that players may temporarily exceed the mob caps, giving enough time for animals to be bred and slaughtered before the creature limits kick in. Specifically, no animal younger than 5 minutes will be counted towards its respective mob cap. Hostile creatures younger than 1 minute will not be purged forcibly, but may still despawn naturally in accordance with vanilla Minecraft spawn mechanics. This should allow well-designed mob grinders to work at their full capacity without impacting other players' game experience.
Please visit the forums for more information about Per-Island Creature Limits.