No, it's priced into most computers. Retail costs over $100 last I checked (and more for pro), though OEMs pay cheaper prices for that sort of volume. There are also sketchy keys available for ~$20.
Sort of? You can install without a key, and other than a little 'watermark' in the corner of the screen (and being prevented from changing the wallpaper) it will get updates and work normally.
there are ebay keys for a couple dollars
For the life of me I cannot understand why would anyone waste their money on such keys. Usually those are volume licenses being sold separately, which is not legal and does not provide you with a valid license. If one is intent on breaking the law anyway, one can save those two bucks and use of the many safe activation methods which do not require installing anything on your machine.