Can I have a certain profile to have a password change policy of 1 year, and other profiles (or the rest) as change every 60 days?
I know you can set it for the entire organization, I need to specify users/profiles.
Since Winter'15, one can set password policy and session time out properties per profile. Below is link to the release notes pertaining to the same.
If you look into single sign on options with SAML and use Salesforce as a Service Provider you could enforce differing password policies on your identity provider as the authentication will be done there, not at Salesforce's end.
But out of the box, it can not be done.
Nope. The closest you can get is this
Create a permission set which has "Password Never Expires", assign this to the users which have a 1 year policy. Then set a reminder for the admins to expiry users with that permission set each year.
Then just implement your 60 day policy as is.
Winter 15 new functionality : password policy on profile level !