For MOSS, there are a number of web parts available that you do not have in WSS 3.0.  These web parts can be used with any site including the My Site function for each individual.  A friend of mine wanted to use a very common one known as the Page Viewer web part for his personal SharePoint site.

So he simply ran through the steps.  He went to Site Actions >> Edit Page.  He selected the zone where he wanted to place his web part and went to the Add Web Part list.  The Page Viewer web part is located in the Miscellaneous section.  When my user went to this section, it wasn’t there!

There was only one web part under Miscellaneous known as Contact Details.   This can be a common issue for any site.  But there is a simple solution.  You need to activate certain functions for sites.  For the purpose of My Sites, here is what you can do.

Go to Site Actions >> Site Settings.

Go to Site Collection features under the Site Collection Administration column.

 
You will see that some features are active and others are not.  
 

If you want to play it safe, activate all of the features.  This will give you the ability to use all the web parts and features that MOSS has to offer. Otherwise, activate the ones you need.

Now when my user went back into editing the page, he found his Page Viewer web part under Miscellaneous and many others. 

For a future reference, if web parts are not available on a Site Collection, have the site collection administrator activate features.