Rabbits,

[Snackish]

Any tips on how to catch these little fast fuckers? they got nikeys.

[mobtown]

corner em.. or just run em down with a horse. lately ive been catching them alive I guess I just got faster not sure so I'm storing 3 rabbits alive till I find out if I can breed them

[Sevenless]

Grassland lets you sprint to catch them, that's one option. Otherwise you gotta get lucky in a forest and find a derp rabbit now that they improve fleeing AI. Some animals of a species move faster or slower than the default speed.

[Scoodles]

Any area where you can sprint makes it easy peasy
In biomes where sprinting isn't an option crawling somewhat close and shooting them with a bow works

[sf17k]

1. Corner rabbit or wait for it to stop
2. Make room in your inventory
3. Drink to refill your stamina
4. Set speed to run
5. Right click the rabbit and the moment it takes off, hit Ctrl-R to sprint (unless the biome won't let you)

Corner it against cliffs and deep water. Don't let it get to shallow water.

[Faraen]

Also if you see any foxes around ,try forcing the rabbit to run into the fox, they will usually catch them and finish them off. Also you can keep a close watch if you will ever see a badger and fox next to each other, they sometimes fight and badger usually wins, giving you free dead fox. Be careful though as badgers can aggro you if you are too close. (you can also try to finish off the wounded badger, but it's quite risky)

[TacoboyRocks]

Get 17 agility. There is a huge difference. You can catch rabbits while running (The third speed tier thing)

[satinembers]

Get a horse. Then you can catch all you want, as well as fill your inventory with dragonflies.