These use cases spring to my mind: real-time data and multi-player action games, perhaps even streaming media.
TCP and HTTP are less than ideal transports when it comes to real time data. In case of a network error, TCP retransmits the lost data but in a real-time environment, the data is already old and therefore next to useless. Real time action games (like quake) favor udp over tcp.
Some questions: Why replace UDP? Why not work on top of UDP? There must be a reason for this. What about multicast?