Hopping Machine

Ambulance all employing the principles of hopping instead of running

Screw wheels, treads or walking. For some robots and vehicles, their sole means of mobility is jumping or hopping around, as silly as that might seem at first glance.

In reality, this is a Justified Trope as this enables robots to actually walk and even climb the stairs without actually having any knees to bend, which simplifies their construction, albeit can leave them vulnerable to falling over.

Comic Books

The Leapfrog from Runaways.

Literature

In the Red Dwarf novel Infinity Welcomes Careful Drivers, cars on the Spanish-owned port of Mimas on one of the moons of Saturn are a variation on the trope: they normally employ wheels but can also use hydraulic legs to leap into the air in order to bypass the city's notorious traffic congestion. The first chapter, in which Lister is scraping a living hotwiring cabs for the night and picking up fares, goes into some detail about the disadvantages of this technology.
In the opening of Heavy Weather by Bruce Sterling, the heroine rescues her brother using one of these. Later, that brother has some drugs and other items smuggled across the border to him using a one-legged hopping robot carrier.
At the end of Bert's Hall of Great Inventions, Bert shows Ernie an electric hopping baby carriage. As in the rest of the book, Ernie is reminded of an animal with similar abilities.

Live-Action TV

Knight Rider: KITT can do something similar to the Red Dwarf example when the situation warrants, which is pretty much Once an Episode.
Mighty Morphin Power Rangers: The Black Frog Ninjazord, naturally, what with being a frog.

Tabletop Games

GURPS 4th edition Ultratech handbook includes, in its chapter on Nanomachines, the "hopper" type—microbots that resemble metallic fleas or crickets.

Video Games

In the RTS game Aztec Wars one of the Aztec military units is a cannon that moves by hopping around on one giant foot.
System Shock features robots called Hoppers, which are Exactly What It Says on the Tin.
Duke Nukem II has hopping, one-eyed robots as one of the enemy types.
Half-assed example: In Lego Star Wars, when C-3P0 gets hit his leg falls off and he hops to get around.
The TX-6 Jumpstart from Prinny: Can I Really Be the Hero. "No one knows if it's supposed to move like that, or if it's just broken."
The Big Eye from Mega Man. Every game of the original series has its own variation of that enemy, of which the one from the first and second game being the worst ones.
The Egg Spring from Sonic Advance.
The spring-like enemies in the Bubble Bobble series. If trapped in a bubble, they tend to take a very short time before breaking out.
Though not technically robots, there are some enemies and statues in The Legend of Zelda that get around by hopping.
The X-Bot from Heavy Weapon. Don't let him hop on your tank, it's a One-Hit Kill!
The Jumper enemies from Mini Robot Wars. They jump over all your units in a fashion similar to the Pogo Zombie from Plants vs. Zombies.
One vehicle from Makai Kingdom hops around on a single springy leg thing. It's even called the Hopster.

Western Animation

One of the Convert-A-Car's alternate forms in the Wacky Races uses 'Pogo Power'.
The Luxo lamp.

Web Comics

Narbonic's Professor Madblood once attempted to build a giant robot, but he only got as far as building a giant robotic foot, which has to move by hopping.
In Sluggy Freelance, Riff's Mark-19 robot can do this, but it only works once.
The above pictured Rabbit Ambulance, from Achewood.

Real Life

The 3D One-Leg Hopper.
Semi-example: Self-Healing Minefield.
One of the proto-helicopters frequently included in the Dawn of Flight Failures Montage is one, albeit not intentionally so.