Cool Sidecar

An option for the Cool Bike, a Cool Sidecar adds another passenger or extra storage to the bike. Normally the rider on the sidecar could just fire on enemies with his or her own weapon while the driver drives, but there are instances where there are things like Cool Guns mounted on them.

Examples of Cool Sidecar include:

Anime and Manga

The Big O: Norman's bike's sidecar has a missile launcher.
Pokémon: Officer Jenny from Viridian City briefly uses a police motorcycle with one of these to get Pikachu to the Pokemon Center.
In all versions of Ah! My Goddess, Keiichi Morisato's BMW motorcycle (the only luxury he owns) has one. Curiously, it was installed to the bike long before Belldandy, its only seen passenger, came into his life.
Wil's bike in Allison & Lillia has a sidecar. (The vehicles in Allison & Lillia are cool by definition because the author chose to include only cool vehicles in that world.) It's even odds on whether Wil rides the bike and Allison is in the sidecar, or Allison Drives Like Crazy and Wil's in the sidecar.

Film

Batman the Movie (1966): After the Penguin steals the Batmobile, Batman and Robin take the Bat-Cycle to Gotham Airport, with Robin riding in a sidecar. As they approach the Bat-Copter, the sidecar detaches a "Go Cart" carrying Robin, which proceeds on its own to the other side of the Bat-Copter.
Henry Jones Sr. & Son do this in The Last Crusade, as shown above.
The sidecar in the Wallace and Gromit short A Close Shave can also double as an airplane. It also comes with a retractable rapid-fire cannon that the heroes usually use to shoot soapy water up onto windows they're cleaning from ground level, but during the climax Gromit loads it with porridge to fight Preston.
In The Spy Who Loved Me, the bad guys chase James Bond with a sidecar that becomes a detachable missle steered by a joystick on the motorbike.
His Excellency's "car", in the Marx Brothers film, Duck Soup. After being twice left behind by Harpo in the detached sidecar, Groucho insists that this time he's driving. Cue Harpo driving off in the sidecar, leaving Groucho on the immobile motorcycle.
In Those Magnificent Men in Their Flying Machines, the German flying machine is out of control, and the American hero is attempting to help by pursuing it with a motorcycle with a sidecar. The German general (Gert Frobe) jumps in the sidecar. When they get close enough, the hero jumps from the motorcycle to the flying machine, leaving the general in the sidecar. Eventually, the cycle and sidecar fly into the sewage farm.
In the On the Buses movies, the family (except for Stan, who drives the bus) has only a motorcycle and sidecar to transport. There are many mishaps.

Literature

Surely the ultimate example: in Neal Stephenson's Snow Crash, Raven rides around on a bike, the sidecar of which is a NUCLEAR WEAPON. A nuclear weapon keyed to explode if his heart stops beating.
In Robert Asprin's Phule's Company, Chocolate Harry rides his hovercycle, with Louis (a small, slug-like alien) in the sidecar—armed with a Sawed-Off Shotgun.

Live Action TV

Kamen Rider Kaixa's Cool Bike, the Side Basshar, had a sidecar. The bike-and-sidecar ensemble could transform into a walker loaded with missiles.
Super Sentai used to add sidecars to non-Red-Rangers' bikes, such as in Kyoryu Sentai Zyuranger (the bikes never really made it to MMPR except for a stock footage slip-up). Epecially notable is the sidecars from Ninja Sentai Kakuranger, which connected end-to-end to form a catapult for launching the Red bike!
- Rescue Sentai Go Go Five / Power Rangers Lightspeed Rescue featured a weaponised example that could be launched at the enemy.
In the cooking show Two Fat Ladies (formerly on Food Network), the ladies toured the country in a motorbike and sidecar. Jennifer Patterson drove the bike while Clarissa Dickson Wright was in the sidecar.
In the On the Buses TV series, the family (except for Stan, who drives the bus) has only a motorcycle and sidecar to transport. There are many mishaps.

Music

To The Apocalypse in Daddy's Sidecar by Abney Park. The song was based on the songwriter's kindergarten-age daughter writing this as a response to the question "If you could be anywhere in the world, where would you like to go?" Let me remind you: this is a 4 year old girl saying this. Of course, "apocalypse" was misspelled.

Tabletop Games

In Warhammer 40K, Space Marines can field assault bikes which have a sidecar with a mounted Big Freaking Gun.

Toys

Bionicle: The Kaxium V3 consists of bike and sidecar, the latter of which has a Thornax Launcher and both can split from each other.
The toys from Transformers: Revenge of the Fallen added a sidecar to the second of the motorcycle Autobots released, which naturally wasn't in the movie. (The sidecar, not the second 'bot...)
- The bike girls had a unicycle design for their robot modes (balanced on one wheel instead of legs.) The sidecar included with the toy for one turned into a stand because it couldn't stand up otherwise.
The toyline for New Batman Adventures eventually had a Batbike and detachable sidecar a la the movie mentioned above (it's Nightwing rather than Robin in the sidecar).

Video Games

Advance Wars: Days of Ruin has the Bike unit that has a sidecar with a machinegun mounted on it.
X-COM: Apocalypse has hoverbikes, with top engines slightly faster and more nimble than the VTOL fighter plane. Its sidecar provides one weapon mount good enough for most of fighters' weapons. As in, an autocannon or missile with miniature fusion warhead.
In Metal Gear Solid 3: Snake Eater, near the end you sit in a side car and gun down Mooks in a pretty epic chase scene. It also contains a lot of ammo.
Wes from Pokémon Colosseum has this attached to his Cool Bike. His Espeon and Umbreon sit there in the beginning, but are demoted to pokeball travel when Wes gets a Sidekick.
An odd example appears in Kingdom Hearts II when, for some reason, Sora and Riku get a space-motorcycle-thing to fight the final boss in one of his many forms. It's less of a sidecar and more of a platform that happens to be on the side of the vehicle, sacrificing basic safety measures for having enough room for Sora to smack things around with his keyblade.

Western Animation

The Piranha from M.A.S.K. was a sidecar that launched from the motorcycle and acted as a one-man submarine.
Transformers Animated: Prowl's Samurai Armor becomes this in vehicle mode.
Metalocalypse has the Murdercycle, with a total of 4 sidecars, 2 on each side, so the whole band can ride it.
- And it takes up three lanes of traffic - how cool is that?
The Aristocats: "You may not believe this, but I think it's a one-wheeled haystack!"