Sometimes it is more important that the data be sent quickly and without pauses than that the stream be reliable. DNS uses UDP because the transaction between a DNS server and client consists of only one packet each way. If the packet is lost, it will be re transmitted at the request of the client.
Similarly, streaming video often uses UDP as a transport protocol because the occasional loss of a packet is acceptable. It is preferable that the image quality suffer as a result of lost packets, rather than the video stream suffer jitter or pauses (lag) as a result of TCP synchronization.
Games also often use UDP, sacrificing engine accuracy for improved speed/user experience.
These and more examples can be found in the relevant portions of the wikipedia article.
EDIT
UDP is used at the transport layer because it is a transport layer protocol. It provides "provides end-to-end communication services for applications" (RFC1122).
Reliability services are optional for transport layer protocols.