So I'm beginning Spanish, and I was wondering- in the sentence "yo voy a mi casa", can you just say "voy a casa"? I know you can omit the pronoun without any worry, but do you have to say "mi casa"?
Yes, you can omit it. The meanings are slightly different.
Voy a mi casa
means I'm going to my house.
Voy a casa
means I'm going home.
As I learned from a comment, the second version doesn't work in all countries, for example, it would apparently be quite unusual in Colombia where people usually include the "mi" and almost always use the preposition "para": "Voy para mi casa".
Adding to the other answers, note that you can omit "mi" from "mi casa" because the meaning can be inferred. In other cases omitting it would be inappropriate or incorrect:
- Where you need to stress "mi":
-- ¿Vamos a mi casa o a tu casa?
-- A mi casa.
- With other nouns: "Voy en auto" and "voy en mi auto" mean (slightly) different things ("I go by car" [maybe a friend's, not by train] and "I go in my car").