I have a $500 limit, and probably below average credit history. Is there a downside to asking for a credit increase?
I'll take a broader view of your question.
Others have said that "the worst thing they can do is say 'no'." But you admit to (probably) having below-average credit.
So, is it bad for them to say no? That depends!
Are you still deserving of the below-average credit? If so, then what would likely happen if you were to get more credit? Overspend more, pay late more, get into trouble more? In that case, it's probably good if they say no to your request.
On the other hand, if you're "on the mend" and trying to improve your credit, then it might hamper you a little bit because your utilization will be higher with a lower credit limit than with a higher credit limit. So, in that case, it might indeed be bad for them to say no.
But these broader points aside, the act of asking for a credit increase won't hurt you.
From what I have read and seen, it should not have any downside simply asking the credit card company for an increase in your credit line. I did this once and was told the increases happen automatically over time on the account, which was true for that account with that company. It did happen automatically over time as the account history length increased also. I assume this might only done though if your credit score is maintained or increased during that time.
Like JohnFx said:
The worst thing they can do is say "No."