For something to do, I built myself a fixed gear a couple months ago. I've ridden freewheel/geared bikes for over 30 years.
Some of the things I like about a fixed gear: It was very neat learning to ride a fixed gear. It gave me something new to learn. I feel like it is very efficient in city traffic. I can slow down or speed up by just pedaling and I don't have to take my hands of the bars all the time to shift or brake (I am running both brakes). My thighs were sore the first few times I rode a fixed gear, so obviously it works a different set of muscles than freewheel riding. Having only one gear is fun and reminds me of being a kid again on my banana seat schwinn knockoff.
I doubt I look very fashionable riding with my business clothes on a fender/rack equipped FG bike with both brakes still functioning.