I'm working on a mod which adds wild spawning/despawning versions of the vanilla passive mobs. I just started working on a copy of the horse and I discovered this "dataWatcher" thing in its code. Apparently it deals with client-server communication and uses a very limited number of IDs, and so it's preferable to use something else. However, because I know nothing about the deeper, gritty level of code I have no idea what I should replace it with. So far I've just worked with simple entities and blocks.

DataWatcher is just Minecraft's easy way of updating the client. The reason it has such a limited number of IDs (31) is because, I believe all the data gets sent in one byte to update everything. Anyway, the way to do this manually, and honestly be way safer in the sense of compatibility with other mods, is packets. In 1.8, packet handling is done using SimpleImpl. When you need to update the client, you just send a packet to the player with the info to update. It's that easy.

If another mod uses the same IDs in the dataWatcher, won't our mods conflict?

I'm pretty sure they would only conflict if two separate entities from two different mods are trying to send an update at the same time on the same ID. Although, diesieben07 would know more on that. I prefer using a manual packet system to avoid any conflicts. 

Alright so, I'm curious on how exactly someone puts their stuff in another person's DataWatcher?

Alright so, I'm curious on how exactly someone puts their stuff in another person's DataWatcher?

Easy - #getDataWatcher() is public, after all, so you could add DataWatcher indexes at any point from anywhere, even though it is very unwise to do so.