My Activities in Salesforce Appear as “Open Activities” Instead of in the “Activity History”

To ensure all your activities show up under the Activity History (as opposed to Open Activities) make sure you have a "Completed" values in the Task Status list and that it's a "Closed" state.

Here is how to check it:
 

1. In SFDC, go to Setup > App Setup > Customize > Activities > Task Field.  Click on Status
   
   
2. In the Task Status Picklist Values list, check if you have a "Completed" value.  If you do have it, skip to step 5.
   
   
3. You need to create the "Completed" value.  Click on the New button
   
   
4. Type in Completed and click on Save
   
   
5. Click the Edit link next to the Completed value
   
   
6. Check the box next to Closed and click on Save.
   
   

Once the steps above are completed, you should now Completed in the list with "Closed" checked like this: