It falls under personal data about someone. Many (but not all) EU countries consider IP addresses to be personal information, and hence "Store it forever for no real reason" is illegal. You need to have a legitimate, legal, reason to store PI, you need the person's unambiguos freely given consent, etc.

There is currently a court case as to whether dynamic IP addresses from ISPs counts as personal information. But static IP address probably count. And all the other information (user X logged in at time Y and send message to other user Z) would be PI too.