Enter the following at the Main Menu:

Unlock All Cities:
Press Triangle, L1, Triangle, L1, Triangle, R1.

Unlock All Bonus Levels:
Press Triangle, L1, Triangle, R1, Triangle, L2, Triangle, R2.

Unlock All Car:
Press Triangle, L2, Triangle, R2, Triangle, L2, Triangle, R2.

Infinite Continues/Infinite Time:
Press Up, Down, Up, Down, Left, Right, Left, Right, Up, Left, Down, Right.

Stage Skip:
Press Up, Down, Up, Down, Left, Right, Left, Right, Down, Left, Up, Right
.

Win 1P Game:
Press Triangle, L2, Triangle, R2, Triangle, L1, Triangle, R1.

Alternate Paint Job:
At main menu press Down, Square, Down, R1, Right, Right, Up, Left, Circle,
Circle, L2, L1.

Hints

New Cars:
In order to get new cars, you have to collect every coin for all of the Rome
levels, Londons levels, and the first three Tokyo levels. These are all of
the cars you are able to get.

The cars are: 
The Geeze for Rome level 1.
P-nut (Mini Cooper) for Rome level 2.
Froggy for Rome level 3.
Super Genius( Smart Car) for London level 1.
Turtle (Beetle Convertable) for London level 2.
Ricochet (Audi TT) for London level 3.
Fang (Mazda MR2 Spyder) for London level 4.
Road Shark (Honda S2000) for London level 5.
Portabello (Lotus Elise) for Tokyo level 1.
Street Eagle (Porsche 911) for Tokyo level 2.
Black Widow (Plymonth Prowler) for Tokyo level 3. 

Thanks to Revolution readers Dr Justin, matt and Matt Murdock!