This was the first cool trick I learned to do.
In artistic cycling they call this trick reverse handlebar seat (figure n. 1017). Doing such a move in a full circle with hands on the handlebars is worth 1 point, hands-free (complete circle hands-free reverse handlebar seat) is worth 1.5 points.
I heard a poster mention fakie. A fakie is much more difficult to do than the reverse handlebar seat. Consider that doing a reverse handlebar seat is really just peddling forward on your bike while turned around. A fakie involves peddling the bike backwards, a way that it was never intended to go. If you can fakie more than 10 feet consistently, I am jealous.
I cannot fakie past 5 feet at best, but I can do the hands-free reverse handlebar seat around the skate park, looking all around me, using hands for whatever, going up and down gradual ramps (so much fun!), and swerving to avoid skaters and little scooter monsters that pop out of nowhere like some type of video game. It makes for good practice!
I ride a fixie BMX, so I'm able to go down hills in a controlled manner without having to use a brake or shove my foot into my tire.. This just involves applying a slight forward peddling resistance to defeat the backwards momentum. I can go backwards downhill at a fast, regular, or very slow pace—steep hills included. It's all very easy to learn once you've got the swing of it.
Another thing I can do in conjunction with this trick is skid (again, very easy for anyone to learn). Yes, on a fixie you can easily do mad skids by just immediately forcing your peddles still. Since your weight is on the bars, it's so much easier to skid. It can have the look of being almost impossible, as people generally don't assume I'm riding a fixie.
A poster remarked about people commenting on the trick. I get people (good skateboarders who can do tricks I could never do) asking me how I do it or complementing me. One person said, "That's such an awesome trick—it never gets old!" Hearing these comments never gets old. I tell these guys that the move is easier than it looks.
This move can lend itself to doing many other tricks. So worth it to learn, IMO. I'd like to learn the reverse handlebar L-shape hold (artistic cycling figure n. 1116). I'll see if I can find an example on YouTube.