Spiked Wheels

You're catching up the other guy's vehicle with your Cool Car, but he won't let that happen since he's a Mook or doesn't want to lose the Wacky Race. So, he's going to smash his car against yours. Not content with simply trying to run you off the road or shove you off the cliff face, he's going for maximum damage. He's placed spikes on his wheels that now act as a cross between a drill and a chainsaw, and will tear your unprotected tires to shreds on contact. A must have for Roman chariots.

Commonly called Boudica spikes (at least in the UK) after the chariots of the "Queen" that fought against the occupying Romans in England around 60AD.

The Other Wiki's article on this here.

Examples of Spiked Wheels include:

Anime and Manga

Bommer (Greiger in the dub) of Yu-Gi-Oh! 5D's has the trap card Chariot Pile with art work featuring a bike with Spiked Wheels. When activated during a Riding Duel, actual spiked wheels appeared on his own D-Wheel.
Crops up in Speed Racer.
Chariot from the Black★Rock Shooter TV anime has these. Note: the wheels are her feet.

Comic Books

In Asterix and the Black Gold, Roman secret agent Dubbleosix's tricked out chariot has retractable scythe blade.
Red Sonja acquires a Boudicca-style chariot, complete with spiked wheels, for leading troops into battle in Queen Sonja #4.

Film

One of the best examples would be the Ben-Hur Chariot Race. This is also the Trope Codifier.
James Bond had a car that popped retractable barbed spikes from the center of his wheels that destroyed enemy tires, originally used on the Aston Martin in Goldfinger.
- In The Living Daylights Bond used Frickin' Laser Beams instead.
Used on Gladiator to cut a fighter's legs.
Taken to an extreme in the Speed Racer movie, where, well 1:57.
Happens in Grease.
It happens in the 1993 The Little Rascals movie during the go cart race scene. The resident Spoiled Brat uses his money-fueled machine to take out Alfalfa's new MacGyvered car.
The movie Death Race had this in abundance, with one vehicle having large enough spikes to go through the car door and kill the people inside.
In the film Alexander by Oliver Stone, scythed chariots are shown charging into Macedonian phalanx during the beginning of Battle of Gaugamela scene.
Hero example: This is one of Arcee's gadgets in Transformers: The Movie. She uses it on the Junkion carrying (in motorcycle mode) another Junkion who is trying to hit her with an axe.

Live Action TV

CSI New York ran into such a car (using Frickin' Laser Beams to evade the police), and James Bond is explicitly referenced.
Top Gear's Jeremy Clarkson attempts to make a better police car by adding some Boudicea spikes on the back wheels. It doesn't work exactly as planned, mainly because he didn't center them properly thus causing epic wheel wobble.
- And when he actually used it on another car it got stuck and the entire wheel was torn off. That is to say, his own wheel.

Jeremy: Something's gone wrong with the handling!

In the Discovery Channel show Doing Da Vinci, the team built Leonardo's design for a scythed chariot and proved the functionality of the weapon.
MythBusters proved that spiked wheels are always effective in a race as long as the design looks reasonable enough to work. Size doesn't matter that much when it comes to damage, but design does matter for reuseablity, with simple pipes with triangles cut into them being effective and reusable far moreso than complicated props.
Deadliest Warrior had a chariot scythe for the Persian Immortals. Although it didn't look lethal according to the doctor, the simulation claimed that it was an effective weapon (13.5% of all kills) and the fight showed it disable the Celt's chariot.

Tabletop Games

In the Warhammer Fantasy Battle Fantasy Battle game, chariots of some races get upgraded with these, increasing the number of enemies they can run down when they charge.

Video Games

Some enemies in Spy Hunter can use these to help force your car off the road.
In Saints Row 2 you can buy them for your cars.
Vigor, the champion of the Nobilian arena in Secret of Evermore, fights from his spiked chariot. The wheels can cause considerable damage. The catch is, you're on foot . . .
The Scythe Chariot is an upgrade of the regular chariot in |Age of Empires I: Rise of Rome.
Wheel Gator's weapon in Mega Man X 2 is just the wheel, with spikes strong enough to dig through earth. The chronologically earlier Nitroman had one that could climb walls (carrying you with it if you held the button).
In the Mario Kart series games, all of Bowser's cars since Double Dash will be decorated with spikes on their wheels.

Western Animation

This was used in the chariot race episode of Phineas and Ferb in a Shout-Out to Ben-Hur.
Used by Nelson in the episode of The Simpsons where he races against Bart.
Turbine, one of the villainous Road Crew in the Ben 10 episode "Ben 4 Good Buddy", has retractable wheel spikes as one of the armaments on her car.
Lockdown from Transformers Animated has spikes on the wheels of his car mode.
The Mask had these on a chariot in "Baby's Wild Ride," which he used to take out some charging bikers. "My chariot's equipped with enough features to make Ben Hur *drool!*"
The Invisible Car from Megamind has these.

Real Life

Leonardo Da Vinci liked to take things to the point where they really weren't the same trope anymore.
Boudicca never actually used these as British charioteers actually played the part of 'battle taxi' for a (noble) warrior, transporting him into the fray and providing a means of escape if it went badly. Eastern forces did use scythed chariots as a shock weapon but they became rapidly obsolete as the professional armies of Macedon and then Rome produced countermeasures.