What mods can you download then use in other peoples servers for Minecraft?

What you are looking for are plug-ins. Unlike mods, these do not add in extra mobs, items or blocks. They simply use commands to do interesting things, or add new functionality with existing things. For example, on the Lord of the Craft server they have many plug-ins, such as magic. To use magic you hold a golden hoe and shift+right click, and it shoots a thunderbolt.

There are many plug-ins for multiplayer servers but I recommend Bukkit, as it is constantly updated and is very widely supported. You simply download Bukkit and install it on your server, then start puttin' those add-ons in yo' server!