When you sign a lease, you're agreeing to certain conditions. You will pay the required amount of rent, park your car in the right spot, put your garbage out on certain days. Your landlord is also agreeing to abide by certain rules. Your lease is your contract, and both sides are responsible for keeping their commitments.
If your landlord isn't keeping up with his side of the agreement, it's within your rights to do something about it. Here are some situations in which the landlord is negligent and it is perfectly acceptable - and legal - to break your lease.
You are without water or heat. You've paid your rent and your utility bills, but you're sitting in your apartment with four sweaters on and you haven't been able to take a shower at your place for a few days. This demands immediate action. It's not like a light bulb that needs to be replaced or a burner on your stove that's not working. If your landlord doesn't fix it, he's breaking your agreement.
There are a few things you can do here. If you've called and complained and nothing is being done, you can call a repair person and have them fix it. You then submit the bill to your landlord and take that amount out of your rent. Say the repair costs $250 and your rent is $750. Submit the bill and $500 rent payment.
You can also leave. He's not meeting his obligation, so you're not obligated to stay. Just make sure everything is documented and you've given him ample time to get repairs done. If the apartment is uninhabitable - i.e., no heat in the winter - you can claim constructive eviction. This means that the apartment was not livable, so you were forced to move. You stop paying rent and must leave the property.
If you are having problems like these with your landlord, it's a good idea to contact Legal Aide or a tenants' rights association in your area. Legal Aide is income-based, so you can get expert advice affordably. Don't stay in a situation that is unhealthy or unsafe if you can possibly help it.