The introduction of HTML5 somewhat has gone viral with everyone caught up in its frenzy. From mobile applications to games, HTML5 is regarded the right kind of solution for creating agile, flexible, multimedia supported platforms. This has prompted many to declare it the end for Flash.
Before HTML5 was introduced and iPhone shipped without Flash support, Flash was being widely used in creating interactive sites, with embedded video and audio which can't be otherwise done by simple HTML codes.
When an entire site was built using Flash it actually interfered with user web experience. The sites were heavier and usage of Flash animation offered no content for the search engine to crawl. HTML5 on the other hand has introduced multimedia content to web pages without heavy plug-ins. The sizes of files are small, it's interoperable and improve overall web experience for users.
But, one may argue whether it is right to discard Flash completely only because a new technology has arrived. Flash was first introduced during 1997, which means it is a sixteen years old technology. During its heydays Flash has allowed developers to explore their creativity in designing Flash animations without any seeming limitations. On the other hand, HTML5 is absolutely new and still at the level of experiments. The stable recommendation for HTML5 is likely to be introduced by the end of 2014. Moreover, it is supported only by few new browsers, when Flash is supported by most browsers and few Androids as well.
Flash once was largely used in creating highly interactive online games that we all have enjoyed before mobile phones started taking the place. The idea, that Flash is dead, however surfaced when Steve Jobs of Apple argued against usage of Flash. Later mobile phone browsers stopped supporting Flash which was a great blow to its popularity. People started to consider that Flash is dead, when only it is on mobile that Flash was no longer acceptable. The future of flash became a self-fulfilling prophecy as developers in numbers shifted from using Flash to more modern HTML5.
Whether Flash has become a thing of past is still a matter of argument depending on how HTML5 replaces the advantages offered by it. It seems like as popularity of mobile phone usage will increase Flash will become more and more, rare. However, it wouldn't be right to declare the end of Flash yet because websites are very different for mobiles and smartphones.
Currently Adobe is working on Stage3D or Flash 11 which will further improve gaming experience on computers. It will support development of 3D game for Flash platforms. They are currently focusing on the gaming niche.
The decision of whether to use HTML or Flash would depend on requirements and purposes. Introduction of HTML5 has given one more option to choose from but it necessarily doesn't mean end of Flash.