To me, your example says: "I forgot about the return value." The way I learned C, if you really, really want to say "I don't care what the return value is" you'd explicitly cast it, nicely documenting your active non-caring about the return value for future code readers:
(void) printf("Hello, World!\n");
Although, in general, ignoring the return value from things like puts() and printf() is a bad idea, for reasons the article makes clear.
And how do I explicitly ignore the other ways C communicates error conditions, like global error variables (eg. errno), inbound error values, errflags in structs?