What do *most* of the non-protein coding genes code for?
As Dr.A points out non coding regions are not generally considered genes
per se if one adheres to the traditional concept of a gene. The non-coding elements of DNA that are thought to be functionally significant fall into several categories.
There are regions which are transcribed and produce RNA strands which have a function other than acting as a template for protein synthesis. These include the hot topic research area of microRNAs as well as RNA elements incorporated into the ribosomal machinery required for protein synthesis and nuclear RNAs important in splicing and other RNA processing steps.
Distinct from these are non-coding regions whose principle function is regulatory. These are regions which function without ever needing to be transcribed. These are generally identified as regions highly conserved across several species which are not transcribed, these are termed Conserved Non-coding Elements (CNEs). While regulatory functions have been showing for a number of CNE for nearby genes in the majority of cases we still don't know what if any function particular CNEs perform.
The other important role for non-coding DNA is in a structural capacity. This would mainly include the highly repetitive DNA sequences as are found at the telomeres. There are also regular DNA sequences associated with the higher order structure of the chromosome through attatchment to the nucleosomes, a multi-protein structure around which DNA is coiled.
The extent to which any of the non-coding regions, although these need not all be exclusively non-coding as some could exist within a coding sequence, could qualify as a gene is debatable. Certainly an NCE with a clear regulatory function could act as a discrete genetic locus for heritable variation with a phenotypic effect and therefore has a good claim to be thought of as a gene.
AS to your other question, people have thought about things such as a field, such as Rupert Sheldrake's morphic field. This is more concerned with the development of multi-cellular organisms than the organisation of proteins within a cell though.
TTFN,
WK