When I started to go out on my bike I felt the need to record it. I bought this inexpensive video camera
The camera is not a top of the range model, you can get this model for around £35. It shoots in 720p, and is shock and waterproof. I made a small plastic holder and used velcro to attach it to the bike. After the run, I would put the video through Adobe After Effects and speed it up with a music track. This is a great budget option, if you wanted to go all out, I would recommend the GoPro or Contour Models.
Here are some of my videos: