Cruis'n World
Bonus Mode
To get bonus mode in championship mode beat all 3 championship courses on beginner and pro levels.
Credit Goes To: Fudgeman( via N64cc

 Bonus Mode
 Race on the Moon
 Secret Cars
 Turbo Boost
Race on the Moon
To race on the Moon you have to beat the WHOLE game including Florida. Beat Florida and you'll see your car get picked up by a helicopter and dropped into a rocket. Then it will show the rocket liftoff into space. You'll land on the Moon and here a man say, "We're cruisn' now!" Wait for the credits to end. When they're finished you'll see a tiny box that says "Moon expert".

Secret Cars
Beat the following times in practice championship mode to obtain a hidden car.

Track         Time          Car
Australia    1:49.00      Surgeon
China        1:14.00      Enforcer   
Egypt        1:07:00      Skool Bus
England      1:46.00      Bulldog  
France       2:15:00      Tommy
Germany      2:27.00      NY Taxi
Hawaii       3:47.00      Monsta    
Japan        2:48.00      Rocket     
Kenya        2:06.00      Conductor  
Mexico       1:46:00      Howler
New York     2:11:00      Grass Hopper
Russia       1:58:00      Rocket
There is also a secret car called the Speed Demon. To get it, you must finish gaining all of the points in the game's Champion mode. This is the fastest car in the game, but it still isn't fast enough to win the Tommy car.

Turbo Boost
When any race is about to start, you'll hear "Ready...Set...Go". As this is starting, hold down the accelerator just after you hear "Set". If you timed right you will get a boost.
Credit Goes To:IGN 64