You will be responsible for the months that you did not give proper notice. You may be month to month now, but it is most likely a continuance of your original lease. Give notice now and at most you will be responsible for 1 month. If you never give notice they may be able to charge you for multiple months. Make sure to do it in writing and maybe even have a witness sign the notice as well. Some shady landlord may decline acknowledgement of the notice. My ex-wife moved from my house by telephone and the landlady declined to admit it until her lawyer got involved.
The previous answer is partially correct. In all most all jurisdictions a reasonable notice of vacancy is required, usually 30 days. This is to get your deposit back as long as there is no damage. Remember without adequate notice the landlords has a right to recovery of his/her losses which could entail more than the 30 days. When sending the notice send it by regular first class mail and certified mail. This little practice constitutes service. On the certified mail put on the bottom this letter is being sent regular mail and on the regular put this letter is being sent certified. That way there is no doubt that they got your notice.