There are quite a few messenger applications out there. Most people prefer BeeJive or IM+ - not only because they promise you to keep you online 24 hours a day - even without having the application open on your iPhone.
Since until today, no application can stay "online" in the background (i.e., if you push the home button on the phone, the current active application will be closed) this means, that BeeJive or ShapeServices (IM+) keep you logged in through one of their servers. This also means that every conversation runs through their servers.
Here is a little overview:
|BeeJive||X||X||X||X||X||X||-||uses their own servers|
|IM+||X||X||X||X||X||X||-||uses their own servers|
|IM+ for Skype||-||-||-||-||-||-||X||direct connection?|
|Fring||X||X||X||X||X||-||X||uses their own servers|