They give you a free dimension pretty early on. It's not much, just a shrine on a hill, but it's mine. Daethrys has picked up a few things in his journeys beyond what he was given to fill it and they've all found a home there. A few more things I bought for it because I wanted him to have a home that looked like one. It isn't much, someday I want to make an alt and try the Dreamweaving profession and maybe make something bigger. But for now:
Lord of the Rings Online has housing too, though it's a bit more annoying needing to pay an upkeep on it. You don't get to really own it, just rent. Still as soon as Sadrondir had the coin he had to have one in the Elven neighborhoods.
And then he gave me -all- of his leftover and extra furniture along with some pieces he'd picked up deliberately for me.