There are too many to list, but I'll give you a few of them.

The Dark Brotherhood quest-line gives two costumes.
The Thieves Guild quest-line gives two costumes, and a pet jackal when you first walk into Abah's Landing.
You get another pet just by walking into the city of Orsinium for the first time.
And you get a dragonfly pet by walking into the Brass Fortress for the first time (Clockwork City).

You can get a robotic spider pet if you do the quest in the Razak's Wheel public dungeon.

If you complete the Mages Guild quest-line, you get two skill points if you sacrifice a character named Valaste at the end. Otherwise you get nothing.

If you complete a ton of the content from Orsinium, you get three costumes. You have to do a billion Wrothgar quests, collect all relics for the museum, kill bosses and a few other things. I did it once, but it was such a chore I don't plan to ever do it again. Here's a link to more info about this: https://forums.elderscrollsonline.com/en/discussion/224059/hero-of-wrothgar-house-of-orsimer-glories-costumes/p1

There are also a few polymorphs you can get in the game.
You can get a skeleton polymorph from a Shadowfen quest in Stillrise Village. (Turns you into a skeleton when you use it.)
You can get another type of skeleton polymorph from the Dark Brotherhood DLC. Here's some info: https://forums.elderscrollsonline.com/en/discussion/262377/litany-of-blood-cadaverous-assassin-polymorph-guide