Yes.
Once you get a certain amount of relationship (70-80 I think) they will give you their house key, which lets you unlock their door and enter whenever you want. Mirel doesn't live in Silverpine so she'll ask to move in with you instead of giving you a key. (She once asked me to move in with her in Thalassar. lol)
Either with key or high relationship with a NPC you can eventually move their furniture, take and storage items in their chests/boxes and build on their land. You might be able to construct and deconstruct their homes as well, but I haven't gone that far or asked yet.
I think you can sleep in their beds, but they usually don't sleep with you unless you talk to them about it first. Otherwise they'll just stand next to you all night or sleep on the floor.