I rent a room out and do not require a lease. My feeling is if anyone is unhappy they can find another place. I only ask for a 30 day notice. My last tenant gave me notice the day they left, saying they were never informed about a 30 day notice. I asked for a $100 deposit, for carpet cleaning when they moved in. They want the deposit back. I don't think they are entitled to it and I in return should be entitled to a months rent. Any advise?

A notice is not assumed, it appears you did not put your rental agreement in writing. So the terms are just that, exactly what you told them when they moved in. While a 30 day notice is common and customary, why would you expect one if you were not clear that it was required.

Also things can depend on where you are at. Since a deposit is in some areas for damage to property, not unpaid rent .

Next since you are renting a room, is your home zoned for multifamily, if not, it is even possible that it is a illegal rental, and the tenant could even ask for his rent money back.

I only say some of these since it appears you did not research the legality of being a landlord and set up things for self protection.

I disagree a bit with Chuck here. In the absence of a written agreement local laws govern and local laws usually require a 30 notice.

Second, while a deposit is generally to protect against damages, it CAN be used to cover unpaid rental. But you need to give them a written notice detailing how the deposit will be applied.

Finally, do not work without a net. You can have a lease that specifies a periodic (month to month) term. This allows renters to move out with notice and still protects you.