Is there a method to search the web for website page sources that mentions WordPress, vbulletin, or Yahoo Site builder? Basically websites using WordPress or something like Yahoo Site builder?
You can use NerdyData to search the page source of the sites it has indexed. Doing a quick test of it on wp-content seems to work fairly well, although returning only ~8.5 million sites means that the NerdyData index is pretty small. WordPress is run by a lot more sites than that. If the site(s) keep the default copyright text (e.g. "Proudly Powered By WordPress"), you can attempt to use Google to see a list of sites that still have the text on there. My initial (and lazy) searches indicate that you will need to work around Google's desire to show you how to remove said default text, though.
The other alternative is to build your own spider and have it look for specific code instances. This is not recommended unless you have a few exabytes of spare disk space handy and a really good bandwidth provider.
It's far, far easier to look at any individual site and figure out what it is built with than to trawl the entire web looking for specific examples.