Until I learnt this tip, whenever I needed some fancy character (£,°,á,ß, etc.) I went hunting for somewhere to copy and paste it from. Not any more!
I assigned my previously useless windows key to be my Compose key. To type the above pound sign I pressed the windows key, then pressed the L key, then pressed the minus key. Scharfes-S (ß) is simply windows key then press the S key twice. To type á (a with an accent) you press ' (shift-7) and a after the window key.
(Note: until I wrote this post I thought you had to hold the Compose key down while pressing the other keys. That works too, but it is easier to treat it as a modal switch. In other words, you press the Compose key to enter Compose Mode, then the next two characters you type are interpreted together. And if the two characters you type have no special meaning then nothing happens. Either way you exit Compose Mode after your two keypresses.)
See here for the full list of all the compose options
Naturally the above is for linux. This page answers how to do it on Windows and here is the same concept on a Mac
Bonus Tip. Ever wanted to write a Japanese post office sign ( 〒 ) ? Enter your Japanese IME and type yuubin (ゆうびん) (then press space). The ～ symbol can be done by typing kara (から).
˙unɟ ɹoɟ ʇsnɾ ˙uʍop ǝpısdn ʇxǝʇ ɹnoʎ suɹnʇ ʇɐɥʇ ǝʇıs ɐ puıɟ :dıʇ snuoq ɹǝɥʇouɐ
(Yes, this is part of Unicode too.)