It also depends what you mean by identified. Bioinformatics groups have cataloged the open reading frames, so we pretty much know where most of the RNAs come from (we think – but see Jack’s post). The trick is to assign function to genes. That will be keeping folks busy for many years. Then there is alternative splicing, which can produce several different protein structures from the same RNA by taking out different parts at the splicing stage. This can lead to proteins with distinct characteristics and sometimes distinct functions. Even if you know one function of an mRNA, there may be more functions of alternative-spliced products of the gene waiting to be identified.
Alternative start codons
Alternative poly-A tailing
RNA editing (such as conversion of a base to inosine)
Association of peptide chains into quartenary structures, with potential for alternative quartenary structures and differences in function
So, if you decide to study molecular biology, there will be work to do for a while.