It is illegal, under federal law, to refuse to rent housing to someone because that person uses a guide, hearing, or service dog. (The Fair Housing Amendments Act, 42 U.S.C. §§ 3601–3619.) State statutes may offer additional protections.
As a practical matter, assistance dogs are normally so well trained and well behaved that a landlord has little reason to object to them, anyway. The law allows landlords to include reasonable regulations in the lease or rental agreement. The owners, like all dog owners, are liable for any damage the dogs cause.
Still, landlords sometimes try to impose a policy of keeping out all animals, even those specifically allowed by law. One company, which owned an apartment complex in Washington, DC, told prospective renters—who were actually testers from the Department of Justice—that no dogs, including guide dogs, were allowed. The company ended up paying $25,000 to compensate would-be tenants who had been discriminated against and another $20,000 penalty to the government. (United States v. Douglass Management, Inc., consent order, 2006.)
Subsidized housing. In some circumstances, people with disabilities who live in government-subsidized housing are allowed by law to have dogs, whether or not the dogs have any special training.
A good resource is Best Friends for Life, a short book that does an excellent job of explaining the rights of people with disabilities (and others) to have animals in rental housing. It's available from the two organizations that published it: