you care about the data, you want it to arrive in order, and you need it arrive. You want to be notified if there is a problem at the other end. You want the data sent to match exactly the data delivered.
File transfer, simple protocols, advanced critical protocols. Anything where the dev doesn't want to think about how to account for packet loss. Its already done for you in a standard interface.
Why you want UDP:
You want the latest packet of data, and you want it now. it doesn't matter if you lose a few packets. Telephony is the classic example. if you loose a frame its not the end of the world. Streaming video is another, Use FEC to cope with loss.
Tedious real world analogy:
When you send a letter or a parcel, you have two options: Send it recorded, and pay slightly more per go, but not have the worry about phoning up the recipient to see if they received it.
However if the letter is of little worth (like a flyer or something similar) then the notification and or guarantee that it has/will arrive is a pointless cost.