Removing unused App IDs from the iOS Developer portal has been impossible, until now that is. The latest changes to the iOS Developer Member Center (finally) allows you to delete them.

First you need to logon on to the Member Center as usual and pick your team if you're a member of more than one team.  This done click on the new "Certificates, Identities & Profiles" section :

which takes you to this all new interface :

Click on "Identifiers" and then "App IDs" :

And a list of App IDs will appear on the right hand side of the screen where you can then click on an individual App ID which will expand to show details of that App ID :

Click on "Settings" to see a more detailed view where you can change the settings for this App ID :

Now, do you see that great-looking "Delete" button down the bottom?  Go ahead and click and this magic prompt appears :

Finally, after over 5 years of waiting, we can finally delete all those junk / test App IDs that we've all created over the years!  Thanks Apple, this is really going to be appreciated!