Why use UDP if it is unreliable?
Two reasons: speed and overhead. UDP packets have almost no overhead--you simply send them then forget about them. And they are fast, because there is no acknowledgement required for each packet. Keep in mind that unreliable doesn't mean that packets can be lost or misdirected for no reason - it simply means that UDP provides no built-in checking and correction mechanism to gracefully deal with losses caused by network congestion or failure.
UDP is appropriate for the many network services that do not require guaranteed delivery. An example of this is a network time service. Consider a time daemon that issues a UDP packet every second so computers on the LAN can synchronize their clocks. If a packet is lost, it's no big deal--the next one will be by in another second and will contain all necessary information to accomplish the task.
A broad class of applications is built on top of UDP using streaming protocols. With streaming protocols, receiving data in real-time is far more important than guaranteeing delivery. Examples of real-time streaming protocols are RealAudio and RealVideo which respectively deliver real-time streaming audio and video over the Internet. The reason a streaming protocol is desired in these cases is because if an audio or video packet is lost, it is much better for the client to see this as noise or "drop-out" in the sound or picture rather than having a long pause while the client software stops the playback, requests the missing data from the server. That would result in a very choppy, bursty playback which most people find unacceptable, and which would place a heavy demand on the server.