The free permit checker runs Permit Advisor without an account. Enter an address, a project type and, if you like, the floor area, stories and a sentence about the work. In about 30 seconds it lists the permits the project needs or likely needs, the agency that issues each one, and the official pages it found them on.
The full list also counts the permits that might apply and the ones to check with the agency. Save the check to your account to see all of them: it becomes a project with the suggestions ready to review, and it doesn't use one of your Permit Advisor runs. A check can be saved for 7 days.
Anyone can run 3 checks a day. If you're already signed in, saving adds the project straight to your account.