It's not always clear cut. However, if you need guaranteed delivery of packets with no loss and in the right sequence then TCP is probably what you want.
On the other hand UDP is appropriate for transmitting short packets of information where the sequence of the information is less important or where the data can fit into a single
packet.
It's also appropriate when you want to broadcast the same information to many users.
Other times, it's appropriate when you are sending sequenced data but if some of it goes
missing you're not too concerned (e.g. a VOIP application).
Some protocols are more complex because what's needed are some (but not all) of the features of TCP, but more than what UDP provides. That's where the application layer has to
implement the additional functionality. In those cases, UDP is also appropriate (e.g. Internet radio, order is important but not every packet needs to get through).
Examples of where it is/could be used
1) A time server broadcasting the correct time to a bunch of machines on a LAN.
2) VOIP protocols
3) DNS lookups
4) Requesting LAN services e.g. where are you?
5) Internet radio
6) and many others...
On unix you can type grep udp /etc/services to get a list of UDP protocols implemented
today... there are hundreds.