What are some real-world examples where one-time-pad encryption is used or can be used? I understood that one-time-pad (OTP) encryption ensures perfect secrecy. However, I couldn't find any real-world examples where an OTP was used.
Also, what are some real-world examples where it won't be suitable to use the OTP.
If you want to have the perfect secrecy then it is the only choice. However, it doesn't have integrity and authentication.

If you want to see when it is used, see OTP at Wikipedia, especially the cold war era.

It is not suitable for modern usage, where a lot of messages is sent/received. The drawback is the necessary condition; key length must be at least message length. Also, you must somehow transmit the OTP key securely, not by encryption. You must trust the carrier or you have to carry yourself.

A simple question arises what will you do when the keystream is depleted? Would you wait for the new key, or you would re-use some part of the keystream? Both have critical results. You will not communicate when needed or OTP will fail, see Crib-Dragging.


Per comment: There is an interesting question on this site; Is there a companion algorithm for OTP to ensure integrity and/or authentication?, asking the companions for integrity and authenticity since the OTP only provides confidentiality. Clearly, If you send your data only encrypted with OTP, the Oscar, the middle man, can modify the message. Of course, if he has no knowledge of the structure of the data, the modifications are random. In the other case, the results can be catastrophic. Save the man can be converted into Kill the man. 

As some said, (most of | sometimes,) the time integrity is more important the confidentiality. You may not need encryption but integrity is almost necessary.