It does depend a lot on which firewall you are using (and how it is configured).
In my experience, I've found ZA tends to give alerts for requests that are perfectly valid. Nothing wrong with ZA doing that of course, as it is rejecting requests that might be invalid.
Personally I've found Sygate to be better in this respect, as most of the time it just quietly logs requests it doesn't like (which includes sites you have explicitly blocked).
However, if your PC is being port scanned (i.e. someone is methodically going through all the ports on your system), then it does produce an alert in the way you described. It also has the option of logging packet data when this happens.