It usually depends how much playing I do, but I tend to change all the strings every few weeks. It certainly does affect, not only the tone, but sometimes the intonation, as strings get worn.
Unlike most of the posters on this thread I dislike brand new strings, they give off too much extraneous noise as my fingers move over them. An hour of playing-in usually settles them down.
One concern with not regularly changing strings is the high risk of a string snapping at a critical moment. Fine if you're a bedroom player, but no good if you're a gigging musician.
If I've ever left a guitar for a long period between changes the state of an old cruddy string makes me shudder and wonder how it made a sound at all!!

C-flat.