There is no law that says you and your spouse must sign a lease when you rent a home together. There's also no law that demands her name goes on the lease if she moves into a house you're already renting. The law does, however, give your landlord some rights too -- and the landlord is within his rights to insist you both sign.
Landlord
From the landlord's viewpoint, it's better if both of you sign the lease. With two signatures, the landlord has two people to pursue if there are problems down the road. If your spouse pays the rent, but loses his job or dies, your signature on the lease means the landlord can try to get the money out of you instead. Even if your family moves out, you may still be liable for the rent check until the lease expires.
Community Property
If you live in a community property state, any debts your spouse incurs during the marriage usually become your debts even if you don't sign a thing. If your spouse is the only name on the lease, and he disappears owing three months back rent, the landlord may be able to sue you for the money. If you divorce, and your spouse agrees to take full responsibility for the debt, the landlord can still try to collect from you if he thinks that will be easier.
Leasehold
Once the two of you sign the lease, your right to live in the house becomes a marital asset. If you break up later, the "leasehold" right has to be divided like any other asset -- unless it expires before the divorce is final. If your spouse gets to keep the house, he should negotiate a new lease as soon as possible. To protect you until then, negotiate an agreement absolving you of any responsibility for the lease. You also need to decide how to divide the security deposit.
Rights
If you've both signed the lease, you share some rights along with your financial responsibilities. Even if your relationship falls apart, you have equal rights to live in the house until you amend the lease. In theory, your spouse could move out, then move back in if she's still a signatory. The best solution is to work it out in the divorce court, where the judge will weigh a fair division of your marital assets.
