Users like that are the ones that keep your jobs as administrators and moderators busy.
The important thing to consider is whether or not the user creates value for the forum. Nobody likes when someone responds to every post -- but adds little in terms of constructive conversation. On the other hand, sometimes the traffic helps keep the conversation going.
In many cases, frequent posters want to be accepted by your community and recognized as a regular. When you "confront" a user like this about posting too much or being annoying, in a sense you are rejecting them, which is bad, which is why dealing with them is a dicey situation.
Giving them something else to do will help to occupy their time, as well as may them feel more welcome.
Of course there is the other type of user, that wants to be the center of attention.
If the user adds value to the forum, try to keep them, but try to break their habit of posting endlessly. If the user doesn't add value, then they are expendable, and you should try to get rid of them in a way that is the least disruptive to your community.
