Removable Turret Gun

"Press B to detach turret"

—Halo 3

Sometimes you need More Dakka, but the turret is fixed to the ground. What do you do? Grab a hold of the gun, steady yourself, and tear the BFG from its mount.

In Video Games, there will most likely the drawback that if the turret gun had Bottomless Magazines when mounted, then the gun would lose that once you detach it, as well as slowing you down.

A Sub-Trope of Improbable Use of a Weapon.

It should be noted however, that many gun emplacements from the Great War/War World Two era (especially plane turrets) were equipped with light machine guns that were designed to be carried.

Examples of Removable Turret Gun include:

Film

In The Mummy Trilogy, the protagonists pluck the mounted machinegun from the plane before it sinks into the quicksand.
In Avatar, Jake makes use of his new body to take a helicopter's mounted M60 while exploring Pandora. It doesn't help.
Flash Gordon: Prince Barin kills a couple of Mooks who are using a machine gun-like energy weapon on a tripod. He picks the gun off the tripod and kicks the tripod away, then continues on using the weapon like a minigun.

Literature

This was the basic plot of Robert Westall's children's novel, The Machine Gunners. In it, a group of English kids find and salvage a working light machine gun from the rear turret of a Heinkel He 111.

Live Action TV

Teal'C did this in Stargate SG-1 by pulling the gun off of a deathglider.

Video Games

Halo 3: you can do this with regular turrets, plasma turrets, and missile pods.
- It may be worth noting that the missile pods are only found as turrets once, in the level The Storm. Usually they are laying around.
Lost Planet: you can detach the VS weapons from the VSs themselves, but you can also attach and reattach them back as you like.
Inverted in Red Alert 3; the Soviets have a mobile unit that can become a permanently fixed turret.
Just Cause and its sequel has stationary Gatling guns Rico can detach and carry around. The gun still has Bottomless Magazines when carried, but Rico's speed is decreased and he can't jump or pick up ammo.
Crackdown 2: when you reach high Strength levels, you can pull off turrets and fire them manually.
Transformers: War for Cybertron not only has these, but also features an Achievement/Trophy for killing 10 enemies with one.
At the time of the game's release, any Sentry Gun the Engineers in Team Fortress 2 put down would be rooted to the ground. If you wanted to move it, you would instead have to demolish it and build a new one from scratch. Come the Engineer update, you can now pick up your sentry and move it in your toolbox instead. The only downside is that it still takes a few seconds to reassemble (albeit faster than the first time assembly), you move slower whilst carrying it, and if you die before your put it down, the entire Sentry blows up.
Deus Ex Human Revolution: if you managed to hack the turrets to shoot at enemies at a computer somewhere else, you can pick them up and move around and kill enemies with it. Also it stays until it gets destroyed.
In Far Cry: Instincts, you can pick up stationary guns once you've acquired Super Strength.
The Laptop Gun from Perfect Dark can be used as a sub-machinegun or deployed as a Sentry Gun.
Justified in the Warhammer 40,000 spin-off Space Marine. The Heavy Bolter is usually mounted on a vehicle or embedded in earthworks to be used by the Imperial Guardsmen, who are just ordinary human soldiers. The player character, however, is a genetically engineered super-soldier who is also wearing Power Armour, and can choose to tear it loose and walk around (albeit slowly) while mowing down everything in his path.
Done in Crysis 2; you better turn the Strength mode on.

Real Life

This was done a number of times by US soldiers in the Pacific during WW 2 by using M1919's taken from aircraft and modifying them for infantry use, so much so that it earned the unofficial designation of "The Stinger". Using the version from aircraft meant that rather than have a rather pedestrian rate of fire of around 500 rpm that the infantry version had, the gunner at his disposal the cripplingly high rate of fire of 1200 rpm. These weapons were generally personally modified from the original turret guns, most notably by MOH recipient Tony Stein. For his weapon he added the stock of an M1 Garand, the sights and bi-pod off of a BAR, a box welded to the side to hold ammunition, and a trigger from god knows where. Using this weapon he was the first man from his unit onto the beach of Iwo Jima, and when his unit became bogged down by MG and mortar fire he single handedly charged to enemy pillboxes, mowing down 20 enemy before he (inevitably with this weapon) ran out of ammo. He then ran back to the beach (barefooted and without a helmet for extra speed) to get more ammo. Eight times. Carrying wounded men on his back.
- As Cracked.com described Tony Stein's weapon: "It's like every gun in the world had sex with every other gun in the world, and then neglected the resulting love-child until it became psychotic and vowed revenge on everything."
In a moment more appropriate to the trope, Mitchell Page and John Basilone were holding the line at Guadalcanal with a tripod-mounted M1917 machine gun, a water-cooled beast that weighs 47 pounds not including the ammunition or the water in the jacket and fires powerful .30-06 rounds (mostly used today for killing deer). At one point, Basilone removed the gun from its tripod and fired it from the hip, and R. Lee Ermey demonstrated it on Lock n' Load to prove to naysayers that it was possible, at least if you're R. Lee Ermey.
A vehicle-to-vehicle version from the mad genius of Soviet military design: GSh-6-30 (30-mm gatling gun that performs well in turrets on ships) installed on MiG-27 (aircraft not specifically built around it). In the CIWS role, it's good - but of course, even a small ship is huge compared to a plane, and the common turret that provides proper cooling and shock absorbing itself weighs a metric ton, while as an aircraft weapon it must travel light. The result: vibration from its recoil is strong enough to shake the plane apart bit by bit (reported forms of damage were so many and bizarre that it's clearly only a question of which parts will happen to break first this time), which often is enough to stop firing before insufficiency of cooling and thus threat of ammunition cooking off becomes the problem - unless it simply jams the gun's own feed first. Very short bursts are viable - as in, usually cause not enough of damage to prevent further firing or mission-kill the plane rather than entirely safe. Dogfight: the Explosive Overclocking edition.