Since WoW does not offer player owned housing, it can be difficult to find somewhere to call home.
Once Garrisons arrive, you will be able to create a whole little village for yourself, but it still might not feel completely natural to your character (if they can't afford it for example).
Claiming and SharingEdit
You can chose to spend most of your time in one certain house in Stormwind and try to claim it as yours, but you will have a very big fight on your hands for it. As it is an MMO, you are sharing the entire world with thousands of other people, and the chances are you will be sharing your house as well. You might be able to work out an arrangement with the others using it but it's unlikely, and new people could turn up at any minute.
It is a lot simpler if you share your space already. Guilds can claim a keep or an area, but must again expect to share it at some point, especially as most keeps have quest givers and vendors and other NPCs in them, so players will drop in from time to time.
RP communities are generally quite good at sharing when it comes to guilds and other large groups of people taking up residence somewhere, but as an individual, you have little claim to anything.
What some people do (myself included) is to use rooms in instances for houses. That way you don't have to share :P
You can pretend to enter a home, and then proceed to travel to an instance (like Karazhan or Black Temple) which offers rooms and other resting areas. Instances are especially usefull if you dislike large crowds and prefer to just RP with a small group of people, and it has no chance of interruptions as you can control who joins you.
The downside to instances is that there's a limit to how many people you can bring, and no chance of spontaneous RP with strangers which can be a lot of fun.