Just because your lease ends doesn't mean your rental has to. Depending on your state's laws, you may be entitled to remain in your apartment or rental home on a month-to-month basis after your lease expires, even if your landlord wants you out. If the landlord doesn't accept your decision, he'll have to go to court to evict you.
Some leases include clauses stating that the landlord must notify you in advance if he's not renewing. If the lease doesn't require that, your state's laws may include a similar clause. In Florida, for example, if you pay rent on a monthly basis, the landlord has to give you notice at least 15 days before the lease expires. In New Jersey, the lease renews automatically unless the landlord gives you a month's advance notice.
Not renewing the lease doesn't necessarily mean the landlord wants you to leave. The end of the lease is the only opportunity the landlord has to renegotiate the terms: It could be he wants you there, but only if you sign a new lease with higher rent or changed conditions. If you don't like the proposed new terms, or if the lease just expires without either of you noticing, that doesn't end your residency -- you become a month-to-month tenant instead.
What happens after the lease expires depends, in part, on state law. In New Jersey, the end of the lease doesn't entitle the landlord to throw you out; she'll have to keep you as a by-the-month tenant unless she has other grounds for evicting you. In other states, the landlord can evict you if you stay on after the lease, but she has to do it by taking you to court. In that case you can stay for however long state evictions take, or longer if she can't prove her case.
Even if you're an unwanted "holdover tenant" after the lease expires, the landlord cannot use any illegal means to get you out. Changing the locks, shutting off the heat or turning off the water are all illegal tactics. If the landlord lets you stay, he will be able to increase your rent, since it's no longer fixed by the lease, but other lease terms continue into the month-to-month period.