On the Arqade (gaming) StackExchange in the “my tags” section the [ios] tag is one of them. I want to get rid of that tag because lots of questions have that tag and I don't want to see questions with that tag when I view the “my tags” filter when you search for questions.
Removing Favourite Tags via Home Page
You can add or remove tags to/from your favourite list, directly from the specific sites home page. You will find this on the right side of the screen. Simply select "edit", and click on the little x icon on the tags you wish to remove.
Removing Favourite Tags via Profile
To remove a tag from your favourite list, you will need to access your user profile. This can be quickly done by clicking on your reputation bar, to the top right.
From here, select "Edit Profile & Settings", and select "Preferences" from the side bar.
Scroll down this page, untill you come to tags. You should see "Favorite Tags", which lists all of the tags you subscribe to. Simply click on the little x button, next to the tag, to remove it.
Note that you can also adds tags to the "Ignored Tags" list, which lets you ignore these questions, or gray them out; dependant on the option you have selected, directly underneath.
Also note that you have to do so from the exchange of which you wish to edit the tags; in your case, Arqade.