Why and when you should avoid using web site templates that are made entirely with Flash ?
You should avoid Flash templates that are made entirely with Flash when it comes to SEO (Search Engines Optimization). When number of visitors that will visit your web page is important, then you should avoid using these templates. Because web pages made entirely with Flash in its HTML code don`t have text that contains keywords and keyphrases that can be read by Search Engine Spiders (software of Search Engines that crawls web pages) - this is necessary for good ranking on Search Engines.
You should use Flash templates that are made entirely with Flash only if number of visitors on your web page isn`t important. If it is not important wheather you will have 1 or 10000 visitors on your web page.
You can use only Flash web templates that contain Flash (.swf) in some portion of them (like some animation, banners, menu, etc...). These web pages in addition to Flash (.swf) file contain HTML code enriched with keywords and keyphrases that can be crawled by Search Engine Spiders. There is no problem in using these kind of templates.

