Do I have to get rid of my mods to play multiplayer?

I have some mods downloaded for a single player world I play on and I was wondering, if I want to play in multiplayer, will I need to get rid of these mods? Similarly, if I have multiple single player worlds with different mods in both, should I have only the mods needed for the world in question in my mods folder? For instance, in one world if had the more enchantments mod and in the other orespawn, would I have to take out the enchantments.jar when I play the orespawn world?

No for multiplayer: you don't have to take them out of the mod folders for servers. Just don't try to do something with the mod or else you'll be kicked by the server or you will crash your client.

yes for singleplayer: If you play singleplayer though you might want to switch the mods out for different worlds as mods will work on any world once they are installed and may have direct influence on world generation. If you then uninstall mods they may corrupt your world to the point you can't recover it or leave you with an unplayable world generation.

Example: uninstalling the better water mod (a mod that replaces all water in a world) on a world that had it installed, will delete all water blocks within any chunk that you have ever loaded.