Fun and a challenge, plus, for me, a great training aid. Having only one gear forces the development of a smooth and powerful pedaling motion. Downhill to maintain a good speed I have to spin up to go fast which means being able to spin at +140rpm. Uphill I have to really push that one gear as I have no option to change gear. Yes you can develop a high cadence and a powerful stroke on a geared bike, but only having that one gear means you can't chicken out.
I rode a 180 mile hilly charity earlier this year on the single speed. It would have been quicker and easier on the geared bike, but I felt great to have finished on the single, Plus the kudos from fellow cyclists is never a bad thing.