You may know that certain keys on your keyboard are dead keys, which create a diacritical character when followed by a letter key, or themselves when pressed twice or followed by a space.
It's nice to be able to type foreign words like ingénue, and I found out that in the X Window System, you can combine the circumflex with other diacritics to produce a double diacritical character, for example ^`a yields ầ. I'm missing a trema dead key on my German keyboard because it provides umlauts directly, and I could only modify ö - ~ö yields ṏ. Still trying to figure out how to type Dutch y with trema, however.
Apart of discovering obscure glyph hacks, I found something of actual use: Circumflex plus number/math operator allows you to type mathematical superscripts. Hence, together with the knowledge of Alt Gr keymaps from my other article, you are now able to correctly denote the proton mass as 1.672621637 × 10⁻²⁷ kg without pasting symbols from an unicode table.