As an Anglo-Saxonist and philologist, I make daily use of a number of characters that are not found on the standard US computer keyboard. These include characters and accented letters from various European languages (e.g. ß, é, ä, ø), IPA symbols (e.g. ŋ, ə, etc.), Middle English ȝ, and various letters and forms used in Old English (æ, þ, ċ, ġ, ƿ, ū, ȳ, etc.).
Fortunately, it is quite easy in X-11 based Linux distributions to create both custom keyboard layouts (for typing individual characters) and custom compose sequences (for building characters from their component parts).