Since this is kind of a generic question, here comes a generic answer.
The important thing from an attacker perspective is the software running "behind" this port. It's a huge difference between an old Microsoft IIS 5.0 or the latest version of Apache but both of them listen on the same port.
Although is true that some ports are more "appealing" than others, since the corresponding services are known to had a lot of problems in the past (for example, ftp, smtp, dns, web...) you really need to fingerprint *what* is running on those ports.
There is a couple of interesting related questions here and here where Marc Ruef presents his cool NSE script.
Best,
Carlos