Under My LInks, My SharePoint Sites, you see a link to a site, but when you click on the link, you are directed to the Access Denied page. It's possible, you may be running into this scenario:
Let's look at a quick example. You have a site collection at http://server/sites/teamsite. You then have a sub web at /sites/teamsite/project1 that inherits permissions from TeamSite. The Profile Synchronization timer job runs at the top of the hour and the users in the TeamSite Members group now have a link under My SharePoint Sites for TeamSite and Project1. Under Project1, you do the following:
At this point, Project1 no longer has the TeamSite SharePoint groups; however, Project1's Viewers, Members, and Owners groups still reference them. When the Profile Synchronization timer job runs, it's unable to determine which users are Members of the sub web and doesn't make any changes. This results in the Project1 link showing up in your My SharePoint Sites menu, but you don't actually have access to the site. Another symptom of this problem is that when you display the Open or Save As dialog in an Office application, you get prompted for authentication daily. This is a result of the Office client synchronizing the My SharePoint Sites information. See this post for more info on how that works. There is also a fix in the Office 2007 Client Hotfix Update from June that avoid the Office clients from prompting for authentication. KB Article 970950.
To fix this issue, you have to assign a SharePoint Group as the Members group on the sub web and all nested subwebs. This allows the Profile Synchronization job to determine which users are Members and clean up the links on the server-side. Once the link is cleaned up on the server-side, the Office client will sync up the next day and remove the link as well. In my testing, if you do not have the above Office hotfix, you will get one last prompt on the client before the link is cleaned up.