And didn't Java and JavaScript also spread pretty fast? Of course, Java was explicitly promoted and advertised by Sun, and JavaScript played off of Java's popularity and later became a web standard.
Smalltalk had a .NET like role in OS/2, one of the reasons SOM even supported metaclasses, just imagine the alternative universe.
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 :)
JavaScript is a really interesting case; initially, I don't think it was really taken very seriously. It was mostly tolerated because of its privileged status as part of the web platform. But since so much has moved from desktop application to the browser, that privileged status has proven all the more valuable!
and with that the Internet. In 1990 UK higher education sites had "high speed" (megabit sometimes!) networking but they used X.25 "Coloured Book" protocols. There were a handful of well developed applications for services such as email, but experimenting with novel software on X.25 was difficult. In 1991 JANET (the people providing these network services to Universities, then and now) began JIPS, an experiment to try out Internet protocols.
Enthusiasm for JIPS was enormous. You could buy or, since you have an electronics department and an essentially inexhaustible supply of nerds, build, a Unix computer, and just like, write your own BSD sockets software. I hear a guy over a CERN has invented a World Wide Web we should check out... In less than a year JIPS ceased to be an "experiment" and by the time I arrived at a University a few years later X.25 was deprecated and few people cared that it was still technically available somewhere.