For my client’s site, they were not interested in My Site and My Links for the first phase. Below are the steps I followed to remove the two links:

1. Log into Central Administration.
2. Under Shared Services Administration in the Quick Launch bar, select the one running My Sites.
3. In the “User Profiles and My Sites” group, click on the “Personalization services permissions” link.
4. For those users you want to remove the personalization functionality, click on the user name (for example, NT AUTHORITY\Authenticated Users).
5. On the “Modify Permissions: Shared Service Rights” page, uncheck “Use personal features”. Click OK to save.
6. I had to shut down my browser and log in again to see my changes.

Note 1: I read on a few blog posts that on the “Modify Permissions: Shared Service Rights” page, “Create personal sites” pertains to My Sites and “Use personal features” pertains to My Links. I could not uncheck all permissions. Unchecking “Use personal features” appeared to modify both My Site and My Links permissions.

Note 2: If you do not change the Administrator user, you will see My Site and My Links displayed. If you don’t want to see them when you log in as an administrator, change the administrator’s permissions.

Note 3: As far as #6 above, this isn’t required. A timer job runs which will switch all authenticated users. Be patient.