People other than your landlord may have the right to enter your rental, including municipal inspectors and police.
While your state may give you significant protections against entry by your landlord, the rules are different when it comes to entry by state or local health, safety, or building inspectors. Generally, inspectors may enter when they have reliable information, such as a complaint from a credible neighbor, that there’s a health or safety problem inside. If you refuse entry, usually they’ll return with a warrant and sometimes a police officer who will make sure that you don’t prevent access.
Many cities run random multidwelling inspections, to catch building and health code violations before tenants complain. You are entitled to reasonable notice (many ordinances specify notice periods). Your refusal to allow the inspectors to enter will simply delay the inevitable.
If the police have a valid search or arrest warrant, you have to let them in. The “notice” period is rather short—about as long as it takes them to knock and announce their presence! In addition, they can enter with no notice at all (forcibly if necessary) in order to interrupt a crime, apprehend a fleeing suspect, prevent the imminent destruction of evidence, or prevent a catastrophe such as a fire. Also, different rules may apply if law enforcement suspects terrorist activity by a tenant.
Aside from the situations explained above, your landlord has no authority to allow anyone into your home without your consent. If your landlord lets in someone who purports to be your long-lost auntie but turns out to be a creative burglar, the landlord will be liable. Landlords who understand the risk they are taking are naturally unwilling to open tenants’ doors for others.