I have read in a book that there are more purine and pyrimidine bases than the basic A, T, G, C, U. For example: Pseudouridine or 5-Methylcytosine. It is also stated, that they occasionally occur in DNA and RNA molecules. I have no qualification in biochemistry, but it would be interesting to know if these rare bases have an impact to synthesis of proteins or the folding of tRNA.
I believe certain bases are modified as a mechanism of self-recognition in the body - apparently this happens a lot as a means of distinguishing human RNA from foreign RNA ( say from bacteria or virus) which actually does not have as many modifications of this sort.