There are a number of ideas why DNA is base 4, but it seems obvious that the principal reason is that it provides a very elegant redundancy mechanism built into the process of replication.
By being in base 4 DNA provides its own backup, which is very important in an environment which thrives on mutation in the long term but also needs to regulate mutation in the short term.
Given that the process of replication can be used as a method for performing calculations, I wonder if it could be abstracted in a non-parallel computing scenario such as a digital computer.
I hate having to deal with backups and bug fixes.