Goat Simulator has mod support, and there are over 150 mods available in the Steam Workshop. I do not use them very often, but here are some that I fondly remember. Since I used mods the most back in 2014 and 2015, some of these may no longer work.
Abu Goat
This mod adds a really cool map based on the Abu Simbel Egyptian temples!
Nyan Goat
This mod lets your goat leave behind a rainbow trail like Nyan Cat.
Ghost Goat
This mod lets you become a ghost and possess NPCs.
Pride Rock
This mod adds a map of Pride Rock from The Lion King. Slow motion mode is activated automatically if you fall off the cliff.
Rainbow Goat
This mod lets your goat change color. You can rotate through colors endlessly or lock on one color. I liked being purple the most. (This and Ghost Goat were made by Geneosis, who has made a crazy amount of high quality Goat Simulator mods.)
This mod adds a map with a ton of trampolines. It's pretty fun to jump around in and see how high up you can get.
Ave Maria
This mod plays Ave Maria whenever you enter slow motion mode. I always thought it was pretty funny.