Is it illegal to have people pay to use your basement for a birthday party?

[BlueDesert]

You don't give us much info to go on. For instance - is this a one time only birthday party..OR..are you thinking of renting it out often just to make some extra cash ?
If it was a once only party for a CLOSE friend I think you can get away with it. If you're thinking of doing it regularly then you have to have local permits and obey all local ordinances. Remember that you are liable for anything bad that happens to any party guests while in your home or on your property.
Probably the biggest thing to consider is if you are thinking of renting it to teens or college-age kids...DON'T DO IT. One of them will announce it on Facebook and you'll have hundreds of uninvited guest crashing the party. Your home could be ruined and there could be violence.
We have had several teens throw parties locally while their parents were out of town. 100's of invited guests show up. Gang-bangers show up.Police are called. It's a nightmare.
I would advise against it TOTALLY unless it's a small party for very young kids (close relatives) that will be heavily chaperoned.