I just moved out of a house that I was renting. There was no lease in writing, only a verbal agreement. Now my landlord is is giving me the run around when I ask for my security deposit. Is this against the law or am I screwed because I don't have anything on paper?

You had a month to month verbal agreement. Assuming you gave them a full 30 day notice that you were moving, and did not leave the place dirty and damaged.
If they don't pay you will have to sue in small claims court.

You can of course always sue, but make sure you don't owe them also. I would assume you have at least a receipt or copy of the check to prove the deposit you gave them

Even with a verbal agreement you still need to give proper notice. If you didn't, then the landlord is entitled to keep your deposit for unpaid rent.

Most states do have laws that state the landlord must return the deposit withn a specific timeframe or a detailed statement of what it was used for. Since you didn't say where you are from we can't tell you the law for your state. There is a sticky at the top of this forum with links to state laws.