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I borrowed this idea from an OOo Writer's extension called Compose special characters: you type two characters, for example a, press a user defined key combination, for example Alt+c and obtain the Greek character α, two dots gives you the ellipsis, =/ gives ≠, … etcetera.
This can be useful, for example, for English speakers that occasionally write words in languages that use accented characters and don't want/don't need to learn a new keyboard layout, or for non English writers that need something outside normal keyboards (in Spanish, the long dash is used in literature).
A useful addition should be an interface for the user to define his/her own "compositions" (something that Compose… do not have).

This is a feature already provided by the OS and is called 'compose' in X11.

Idea marked as implemented.

BUT (unless I'm missing something) you cannot use that to enter non Latin characters (in my example I used greek characters, for example, and none of the tables I can find in Internet gives Greek characters as a choice), nor you have access to the full unicode range.
The compose under X11 solve many user cases, but not all.
My proposal is about giving the user the ability to choose which characters with which shotcuts.

In TeXmacs there is a very simple iterative way.
For example:
First you insert a | then a tab. You'll se a mathematical or. You press tab again und you'll see a mathematical disjunction.
a+tab is an alpha, A+tab an Alpha... &+tab a mathematical and...

After playing with X11's compose for a while I can confirm that you cannot enter non Latin characters with a Latin keyboard, and switching to a Greek keyboard just to insert one or two "alphas" on each paragraph is like killing ants with a machine gun...
For me, this idea is NOT implemented.

I changed the idea tag to "Calligra"