JavaScript was a web standard right from the beginning. Its popularity grew together with the web itself by virtue of being the only programming language that could be counted on to be available on websites.

Flash and Java both required plugins, didn't integrate well with the rest of the website, were quite heavyweight, and frequently got bad publicity due to security bugs.

Of course, browsers themselves also had them aplenty, but at the end of the day one can't use the internet without one :)