I do agree with the other posters - whether butches are a dying breed may depend upon where you are. I lived in DC for eight years and there were lots of butches. The butch-femme dynamic was a relatively common thing, especially the pinup femme + dapper butch pairing. Butch on butch was equally common.
Here in Houston, TX, butches seem to be much less prevalent, though not completely extinct. From my observations, there are plenty of people here who I'd say were somewhere in the middle.
I also agree that self-identifying as butch is not as common as it used to be. The butch-presenting people of my generation (I'm 28) have many more words to describe themselves. Terms like "stud," "boi," "genderqueer," and "androgyne" were not around for the generations before me. Some of the people who identify as the aforementioned terms also identify as butch and some people can find a version of the dynamic without the label.
However, I have met several masculine-of-center folks who have a deep aversion to the word "butch" despite looking the part and oftentimes "playing" it, too. They seem to dislike the implications of the word or feel it's not quite their word for some other reason.
I personally embrace the term butch (as well as genderqueer/transgender to represent my alternate gender identity and androgyne - by the dictionary definition - to describe my physical appearance) because I am a queer history buff and I appreciate the path the butches of old paved for the butches of my generation to be more readily accepted and because butch means masculine, which I am.
I (and plenty of other butches, I'm sure) have sometimes felt
femmes were a dying breed. This has caused me to date my share of feminine-looking women who are usually bisexual and don't actively claim the term "femme" even if they mesh well with me.
I am more than a little old fashioned in some ways and the complete opposite of traditional in others. When it comes to the dynamic I have with a femme, I am what some would define as an old school butch and I definitely try to be a gentleman...