Is it viable to make complete websites out of just flash, or the majority of it being compossed of flash?

Seems like most of the big name companies incorporate flash either wholy or in a major way on thier sites. At least some big companies with really professional looking and neatly interactive sites.

So is it possible to think that one could make a whole site completely or almost all out of flash or not?

Yes it's possible.
Whether you should or not is entirely dependant on how you treat an on-line business

If it is secondary or you have one because ...

... then all flash is Ok (sort of)

BUT if you rely on the online business to bring in orders and enquiries as repeat business ... An all flash site is ABSOLUTELY not ok.

Flash is good to use in your site, however do have in mind if you want to attract customers then text and flash would be the way. Just flash might not bring you many customers.

Yes you can make websites completely out of flash and for some sites like portfolios or interactive sites it is good. However, like chrishirst said, if you are an online business and you want to bring in business from online then flash is not the way to go.

Up until a couple weeks ago, flash content was not really even visible to search engines so your chances of getting indexed were slim to none. Now thanks to adobe providing Google and Yahoo with its flash backend coding structure, flash content and links can now be read however a flash website is still just like a file being called. This basically means you only have one page to optimize and get indexed so you can't really optimize different pages for different keywords.

Flash is also well known for long load times. most people do not like to wait longer than a few seconds for a website to load.

So overall i would not recommend using flash to build entire websites except for certain kinds of sites. There are some pretty sweet things you can do with flash though that you can't do with anything else. So with that in mind it is usually cool to make the menu or your header or just an individual piece out of flash to put into your HTML or PHP code.

Adobe recently announced that search spiders will be able to crawl flash objects, so you may see more "flash oriented" sites in the near future.

I do have to agree with everyone else, for the time being, don't use flash for e-commerce.

Flash can be a pain when building a site based on a database, as it can easily become unmanageable. I much prefer to do simple effects with Javascript, and only allow Flash for music, video, or complex animation.

I'd say that Flash is not viable for most sites, but it can be very effective for more 'abstract' sites, (usually with other sites) that turn say, a car advertising site, into a game/adventure/interactive dream, and then it really works. But you've got to be careful.