Non-phonetic alphabets?

Can anyone here think of a reason for a language to develop a kind of
non-phonetic alphabet--that is, one having no relation whatever to the way
it is spoken?

The only ways I can think of it might occur are
- pictograms (not actually alphabetic, but...)
- a kind of extreme borrowing (the written language borrowed entirely from
an other, preferably unrelated language).

So, perhaps a revision to the question:  Can anyone think up another way of
writing that doesn't refer to the following?

1) the sounds spoken in the language [for <sat>, read "sat"]
2) [possibly stylized] visual representation [for a picture of an apple,
read "apple"]
3) words as spoken/written in another language [for <e.g.>, read "for
example"]


    *Muke!