It is not possible to buy a house in Morrowind. However, NPCs may offer tasks that result in a place to call home. It is also possible to kill an owner and take over a house, though this can cause issues with completing certain quests.
Great Houses provide a Stronghold at either Rethan Manor, Indarys Manor, or Tel Uvirith. Great Houses and other factions also provide a free hostel, which often includes storage containers (though items will technically become "owned" by the NPC owner when items are placed in these containers, flagging them as stolen flag when retrieved later).
Listed below are the towns and other areas from which a house can be made, so you may simply choose the place, finish the related quest or kill the owner, then make it your own.
- Caldera Homes — Small mining town at the foothills of Red Mountain
- Ald'ruhn Homes — The council seat of House Redoran in the dusty Ashlands
- Sadrith Mora Homes — The large, Telvanni-influenced mushroom town on Azura's Coast
- Balmora Homes — The council seat of House Hlaalu on the Bitter Coast
- Pelagiad Homes — The small village that has grown up near an Imperial Fort
- Suran Homes — Relatively small Hlaalu governed city in Southern Morrowind
- Seyda Neen Homes — Live the small-town life in the entry point of Seyda Neen
- Vivec Homes — The largest city in Vvardenfell, a canaled metropolis composed of nine cantons