Humidity in a basement is a problem that tends to get worse, not solve itself. What you're seeing now is probably not the worst-case scenario, but the critical point is that electrical panels are designed to operate dry, and once moisture gets in, the contacts start to oxidize slowly. This can happen for weeks or months without you noticing anything, but the risk of failure increases the whole time.
What most of the answers above point out is valid: yes, you need an electrician. But before you call, check if there's something obvious causing the humidity in the basement itself - a crack in the wall, leaking pipes, poor drainage. If the problem's coming from outside, the electrician can dry out the panel, but the moisture comes back. On the other hand, if it's a specific issue, you fix it and you're done.
While you wait for the electrician, keep the panel open if you can (just look at it, don't touch anything) so air circulates. A dehumidifier in the basement also helps a lot if it's serious. But don't put off calling - one week maximum should be your limit.