Can we use non-gravatar avatars?
Changing your profile picture is a hassle on Stack Overflow. It redirects to Gravatar.
Can't it be implemented like on Facebook or Google+, in much easier way?
Not the most ideal solution but better than nothing. You could specify different email address tags to your email address to effectively give you different hashes (and therefore different avatars). Of course this assumes your email provider supports this. No need to register a different email address at gravatar, you can just use one.
I do something like this:
Then just attach the desired avatars for each and register those emails for the sites. i.e., Set my Stack Overflow email to:
firstname.lastname@example.org, Gaming.SE to