Yes and no. The OS is free, using the 'Android' name is not free as in speech, but (I think) free as in beer, as it does require compliance with Google's Compatibility Definition Document (CDD). See http://en.wikipedia.org/wiki/Android_(operating_system)#Lice...

Shipping Google's applications (GMail, Maps, Google's store; maybe others) requires a license from Google. That probably is not free as in beer, either, but I find it hard to find definitive statements for that on the web. developer.android.com seems to only target software developers.

Also, some technologies used in Android are patented, and require payments to patent holders.

So, in practice, Android is not free for smartphone makers.