Here are a couple of my fixed/singlespeeds.
The first one is my Robin Hood fixed gear. Old brand made by Raleigh. Not sure how old. I'm thinking late '60's or early '70's. Suzue flip flop with19 tooth cog (was 18-didn't feel right). Stronglight cranks with 52 tooth chainring. I cheated and put on a front brake. One of my favorite bikes.
The second is my Lemond Chambray single speed. One of the guys at work gave me the frame. A customer gave him the frame. Frame's good but paint is all screwed up. Vertical dropouts but I played around with the gearing and was able to use a 39x14 combination with no tensioner. Nice for short rides around the park.
The last is my single speed mountain bike. It's an old GT with track dropouts. Surly Fixer with a 18 tooth freewheel. I've got a 34 and a 44 chainring on the front. Depending on the terrain, I can take/add links (two SRAM master links). Something different just for fun.