There are a few.
Generally your go-to word is "villa". Technically it refers to a specific building design (for rich people), but it maps fairly well to our modern multi-room heated home with running water idea.
"Casa" is sometimes translated as "cottage" or "shack" - think a single-room, open firepit hut for peasants. The lower classes might also live in an "Insula", or apartment building.
"Domus" is the word for home, but for whatever reason, i haven't seen it used much.