I am looking for a way to allow users from different sites
to login with their respective username/id.
An example can be seen on this page
Is there something like this for free for WordPress?
For self-hosted WordPress or WordPress.com? (The former is really off-topic for this site.)
Self-hosted, there is this plugin, which allows visitors to use OpenID to identify themselves to register, log in, and leave comments.
For WordPress.com, you can use your blog as an OpenID provider for other sites. You can see the sites where you use this under Settings | OpenID. There's not a way to use OpenID to log in, however.
Another good plugin is http://wordpress.org/extend/plugins/rpx/