Yes, we do use Flash when it's required. There are times when Flash animations can be an asset, but there are other times when it is not. For example, we never use Flash to create an entire website or even entire pages. Search engines are not able to read the content of Flash and, as a result, words used in animations are not indexed.
It is best to use Flash for small banners, advertisements or demonstrations. Other animations should include some written text in the HTML so that search engines will be able to index the information on the site.