Living with the person you love means introducing a new level of intimacy, and it requires a good foundation. Some signs that you've built that foundation include:
You know each other very, very well.
While urban relationship myths claim otherwise, moving in with someone you've known for three weeks almost never works out. Even in the movies. A successful commitment requires knowing what you're getting into, and that takes time. Some experts say at least six months; others say at least a year -- basically however long it takes for the "honeymoon phase" to end. (If all you know about your partner is his or her preferred thread count, you're not ready to share a lease.)
You spend most nights together already.
For most couples who successfully merge living spaces, part of the work was done before the big move. If you already spend five or six nights a week together, and each have the proverbial (or literal) drawer at each other's place, and your relationship is going strong under those conditions, you have a halfway decent indication that living together will be a step toward something even stronger.
You've argued and worked it out.
You don't know how solid your relationship is until you've tested it. If you've never had a fight, it doesn't mean you're a perfect couple; it means you haven't been together long enough to know what kind of couple you are. Living together inevitably means conflict, and you better find out if your relationship can weather it before you sign a lease.
You've taken a vacation together -- and enjoyed it.
As far as relationship-testers, travel has two things going for it: financial issues and stress. If you can not only weather but also thrive on vacation as a couple, you have a better idea that you can do the same in a shared space.
You're able to discuss all of these signs.
If you don't see every one of these signs in your relationship, it doesn't necessarily mean you're not ready (and vice versa). However, if you can't at least talk about each of these topics, and talk openly about them, that's a pretty strong indication you're not prepared to take the next step.
These signs are fairly straightforward. Either you see them or you don't. There are some other issues that require a bit more abstract thought.