Hi megachris,
You’re on the right track, you’re just looking at the wrong screen. If you would like to remove a tab, you need to remove it from the tab group. To do this, navigate to Customize > Tab Groups and select Edit… next to the tab group that you want to remove the tab from. The default tab group is CRM and this is where you will find the Campaigns tab. From the edit screen, navigate to step 2 to and select the Remove link next to the tab that you want to remove.
Then select Finish and that’s it! If you change your mind, you can simply add the tab back from the same screen and step.
I hope this helps.
-Audisho