What applications of clients use bitcoin JSON-RPC?
As far as I understood, the Bitcoin JSON-RPC is one of the ways (if
  not the only way) in which applications can be built that can access
  the bitcoin wallet.


There is also a REST interface, but that is for read-only type commands like getting blocks or transaction info.


  So far, I have just figured our that only bitcoin-cli is such a local
  application which uses the RPC.


bitcoin-cli is just a cli interface to the RPC, it doesn't really do anything on it's own. Also, the RPC interface isn't just for wallet commands. A list of commands can be found in the documentation at https://bitcoincore.org/en/doc/0.16.2/. The commands expose functionality including:


blockchain
control
generating
mining
network
rawtransactions
util
wallet



  Are there any other examples where the JSON-RPC is used?


Many software libraries will communicate with the Bitcoin Core RPC, too many to list, but this might be a good start: https://github.com/igorbarinov/awesome-bitcoin. Not all use the Bitcoin core RPC, some implement their own full node (like copay).