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