Remember: It ain't a mystery if its been solved.
For me the greatest mystery is life itself. Not lifeforms, DNA, genome, etc. but the actual spark or whatever it is that animates what is basically a few grains of dust. Until we figure it out I can't see something like life being created in a lab. We can probably build it but can't get it to run.
Please, if you will, feel free to indicate what you feel is the greatest mystery of all time.