First, you need to understand that there are two types of Google account. Google Apps accounts and so-called 'Consumer' accounts. All firstname.lastname@example.org (or xxx@googlemail) accounts are consumer accounts. Any Google account which has been created by going to https://www.google.com/accounts/ and associating an email address with a Google account is also a consumer account. Google accounts that have been created as part of a Google Apps domain are Google Apps accounts.
Likewise there are two types of Google site. Sites that have been created within a Google Apps domain and sites that have been created by a consumer account at sites.google.com
The two types of site can be recognised by the different construction of the site address (URL) that can be seen in the browser address bar. i.e.
For a non-Google Apps Google account
The Sites that are displayed when you are signed in with a consumer account and go to sites.google.com are Sites where you are listed in the Site permissions as a viewer OR editor OR owner AND the site is NOT a Google Apps site.
The Sites that are displayed when you are signed in with a Google Apps account and you go to sites.google.com (automatically redirects to https://sites.google.com/a/domainname) or when you go directly to https://sites.google.com/a/domainname are Sites in that Google Apps domain only where you are listed in the Site permissions as a viewer OR editor OR owner.
(To see Sites shared with you that do not belong to that domain when you are signed in with a Google Apps domain account, goto https://sites.google.com/site/sites/)
NB. in both cases, the user has to be listed by name. If they are a Viewer/Editor/Owner because they are a member of a group which has that access level, the site will not appear in their My Sites list.
To see all the Sites that are available to you within a given domain, go to sites.google.com, and click on Browse Sites.