Most SEOs will tell you that if your site is built in Flash it will essentially be invisible to Google (and most other search engines).
Thats about to change as Google has announced improved indexing of Flash-based content.
However, as e-Consultancy quite rightly point out, designers should not see this as a reason to build websites totally from Flash: Google still cannot use the tag structure as it can with HTML to work out the importance of keywords through their use in titles, headings and links, so Flash should still be used sparingly.
Also, designers often create Flash-based sites that “re-invent the wheel” when it comes to user interface design, often making sites difficult to use and usually in-accessible to those with disabilities. You also often cannot link to a page within a Flash site as they are all essentially part of the same page.