At the character select screen, after you select your character, but before the game starts hit L+R+Start three times quickly. You will now be able to drive a fast taxi bike. If you can't get this trick to work -- you can also gain access to the bike once you beat all Crazy Box challenges. Simply press D-Up at the select screen to get it.
No Arrow or Destination Markers
This chode allows you to play without arrows, destination markers, or both. If you want to switch off the arrows, press and hold R+Start before the driver select screen appears. To play without destination markers, just press and hold L+Start before the driver select screen comes up. And to switch off both at the same time, simply hold down both L+Start and R+Start before the driver select screen.
Atternate Viewpoints and Speedometer
Plug a controller into controller port #3, then press the Start button on that controller after you started a game in Original or Arcade mode. You can toggle to a first-person view by pressing B (switch back to normal view with A), get an alternate viewing angle with Y, or tap X five times to bring up a speedometer display.
Another Day Mode
Press R at the driver select screen, then press and hold R again while you select your crazy cabbie of choice. You will now see the words "Another Day" appear on screen, followed by a car horn. This will change the game slightly with new fare locations and altered starting positions.
For even more cheats, keep an eye on: Crazy Taxi Homepage