Is the function of adjacent genes correlated?
In bacteria, this is often true.  This is because more than one gene is often transcribed onto a single RNA.  This grouping of genes is called an operon.  It is usually true that these have a related function because they are being translated to protein in very much the same proportion - a convenient way to regulate the function as a whole. 

Once you get into eukaryotes this is no longer true (except for v. rare cases most of which are viral genes), one mRNA transcript contains just one translation region.  This is true even for yeast and other single celled organisms.  Gene regulation can be correlated, but the relationship on the genome has little to do with it.  

There is some importance to the genomic relationship of two genes because of the crossing over that occurs in meiosis, but this is more of a relationship that is important in speciation and evolution, it doesn't have any recognized importance to how the genes act within the eukaryotic cell.