Simple answer: when it is easier to write the rules describing your grammar than to write code that accepts the language described by your grammar.
If the only thing you need to parse looks exactly like what you've written above, then I would say you could just write it by hand.
More generally speaking, I would say that most regular languages could be parsed more quickly by hand (using a regular expression).
If you are parsing a context-free language with lots of rules and productions, ANTLR (or other parser generators) can make life much easier.
Also, if you have a simple language that you expect to grow more complicated in the future, it will be easier to add rule descriptions to an ANTLR grammar than to build them into a hand-coded parser.