All matching an IP address really tells you (assuming it isn't spoofed), is that you share an ISP with the machine that created that traffic.
Here's a real-world example from just this week. I'm a moderator on a site on the StackExchange network. We had a problem user who was posting a bunch of stuff the community didn't want posted (consistently badly moderated). What I'm supposed to do in this circumstance is point said user to our instructions for writing acceptable posts. However, such users often are just sock-puppet accounts for someone who's already been suspended. If that's the case, I'm supposed to take more drastic action.
SE has a (community-mod only) link for this, that shows you the user's IP, and all user accounts that have used that user's same IP. I click on this, and discover that he happens to share an IP with one of our better users. Not only is the writing style completely different (writing style is practically a fingerprint), but this user has in fact voted to close all but one post the problem user has ever made.
I talked to the "good" user about this, and he confirmed that his work access point is shared by a very large number of other people.
Just this week we got another new problem user. Again, totally different style than the other two users mentioned above, but also same IP.
As an investigative tool, IP address is useful, but only as a piece of evidence. I'd place it somewhere down with blood-type (perhaps like sharing an uncommon blood type like AB), rather than up in the realm of fingerprints.