Matt Cutts (a well known Google employee) recently addressed this issue in one of his video talks. According to him Google knows that many sites share IP addresses and you shouldn't worry as an average webmaster. So from the SEO point of view there is no reason, unless you are actively involved in black-hat SEO and don't want Google or other search engines to detect it.

It might however, that some other users on the same IP address are active in spamming. Or maybe some site on the shared IP address was hacked and used for bad purposes. If this causes the shared IP address to be put in one of the IP black lists, that can cause problems. Your emails sent from that server might be blocked by SPAM filters for example. For this reason a private IP address is an advantage.