Guitarist Guild: A Musical Community Beyond Strings

Do new guitar strings really make a big difference to the tone of your guitar? I mean I play at home for a hobby only, and rarely change strings until I break one.  So don't really notice any slow degradation of the tone.

Should I be changing them more often regardless of breakages?

Here's what I do: when first one breaks I change the set. When I was gigging I bought a new set for my bass every few months, but the guitar players would change theirs far more often.

As a hobby player now I hardly ever change the strings on my basses, but they no longer get anything like the same beating they used to get. In order to keep the strings on both my guitars and basses in reasonable condition I always wipe them down carefully with a dry lint free cloth after every play - the salts in even a small amount of sweat will destroy the tone of strings in very short order.

Old and degraded strings sound very dull.

Am I correct to assume that newer strings tend to get out of tune more than older one due to stretching?