Minecraft – Slimeballs on the surface

Any mob trap within 16 blocks of the bottom of the map will catch slimes as well, but you have to be careful to not hurt the slimes too much to get them to split the most. Punching and drowning are the safest ways to ensure that they'll split into more slimes. Also, you want a large room so that bigger slimes will spawn which can then have more splits.

The most important thing besides the depth is that it's in a chunk suitable for slimes. Slimes can only spawn in 10% of the chunks, picked randomly depending on the seed. You can calculate which chunks are suitable with this tool by trunkz though: http://www.minecraftforum.net/topic/397835-find-slime-spawning-chunks/

They only spawn a tenth as often as other mobs, but they'll also spawn in any light level, so if you're digging for diamonds at bedrock level, you'll usually find quite a few naturally.

I know that this question was asked a long time ago, but just thought I'd give an update and a correction for future people that read this. (please consider that things may also change in future)

Ok, so first of all, you mentioned that a Chunk is 16x16 block around the player. This is incorrect. A chunk is a section of the terrain and is nothing to do with where the player is. The chunk does not move. A chunk is a 16x16x256 (W,D,H). So for the mob spawning. The quote you gave is correct, however, does not note that it is centred around the chunk that the player is standing on. So 7 chunks in every direction from the border of the chunk you are standing in.

And now for your question :) Recently, (not sure when it started) height has become even more important for mob spawning and each chunk is split into segments. This is to reduce the amount the game has to render and does this by going up in 16 block segments starting from 1. So 17, 33, 49, etc. This is called the lc value and can be shown on the debug screen (F3). It is important for mob spawning, why? Because any segments in the chunk above the maximum segment that has anything other than air in do not get checked for spawning conditions. This therefore means that there are many less blocks to check which in theory will make your mob grinder or xp farm more efficient.

There is a fair amount more... however, I think this answers what you wanted. At least I hope it does ;) Best of luck guys.