Mobile Kiosk

Sometimes The Little Shop That Wasn't There Yesterday has a very good reason for disappearing and reappearing at will: it has a motor!

A Mobile Kiosk would be any device where the owner sells something with the additional benefit that when business dries up he can pick up and move. Perhaps a conman with a collapsible table, a bazaar merchant with his store on a cart, or a hoverskift selling fresh alien fish. See Travel Cool for more odd vehicles such as Fruit Carts.

Examples of Mobile Kiosk include:

Anime and Manga

The theft of a yatai (Japan's version of the trope) meant as a dowry is the driving impetus in Ukyo's Backstory in Ranma ½.
The elusive "Neko Ramen" stand plays an important role in the first episode of The Tatami Galaxy and shows up from time to time later in the series.

Film

The Vending skiff from The Fifth Element.
The opening scene of Guys and Dolls has a pitchman and his female accomplice whose pitch is a box with fixed legs.
Doctor Terminus' "Landship" from Pete's Dragon
Bedknobs and Broomsticks: everything in Portobello Road that isn't nailed down. As well as Professor Browne's nifty suitcase act.
The vendor in the film Top Secret!.
At one point in Brain Donors, Cloudcuckoolander Jacques produces and expands a collapsible office desk, complete with collapsible computer, collapsible printer, and inflatable secretary.
Luz's taco van in Machete.

Literature

Jean Merrill's children's book The Pushcart War. Pushcart vendors vs. monster trucks!
Discworld has C.M.O.T. Dibbler, who uses a handcart when business is going well (when it isn't, he just has a tray round his neck). In Making Money, it's suggested that he might want to invest in an actual storefront, but he replies that in his business it pays to keep mobile.
- In Wyrd Sisters, written before Dibbler was created, the narrator speculated that hot-dog stalls incorporate small, gas-powered time machines, enabling them to appear out of nowhere whenever a crowd forms.
- Dibbler's counterparts elsewhere on the Disc have similar carts or trays. The Ecksian version, Fair Gos Dibbler, calls his tray Dibbler's Cafe de Feet, a parody of the famous Sydney meat-pie van Harry's Cafe de Wheels.
Abie Glassman in The Great Brain.
Dr. Seuss's The Sneetches and Other Stories gives us Sylvester McMonkey McBean and his portable Star-On and Star-Off machines.
Ignatius J. Reilly spends time pushing around a "Paradise Vendors" hot-dog cart in A Confederacy of Dunces. He usually eats most of the hot-dogs himself, only barely selling enough to make up for his own consumption.

Live-Action TV

The Twilight Zone TOS episode "One for the Angels". Lew Bookman has a mobile pitch: a suitcase with extensible legs. When he finishes a pitch, he collapses the legs back into the suitcase and moves on.
In season 3 of The Wire, Bubbles starts selling white t-shirts to the drug dealers and users around Baltimore from a shopping trolley. Later in the season and in season four he starts to expand his operation, offering cans of paint, pirated DVDs and other such assorted goods from his trolley.
Tin Man: Demilo's ungodly tacky whorehouse-on-wheels
An entire town does this in one episode of The Adventures of Superman, in order to fleece passerby with phony speeding tickets.
One of the odder challengers in the Japanese version of Iron Chef was a chef who was cooking out of one of these who brought it into the arena with him. Did fairly well too.

Tabletop Games

Shadowrun: often has mobile medical care facilities and repair shops for the "don't ask questions" type. Of particular note is DocWagon, which -- if you are a subscriber -- will send an armed medical team to extract and treat you when your automatic life-signals monitor indicates you're in serious trouble.

Theatre

In Oklahoma!, Ali Hakim the peddler has one of these.

Web Original

Homestar Runner: Every summer, Bubs drives around in a van selling... baloney sandwiches.

BUUUUUUHHHHH-LO-NAAAAYYYY!

Western Animation

The Simpsons, when Marge started a pretzel business and drove around with the pretzels in her station wagon, her rivals had a falafel truck.
- In The Simpsons various times when they go to "ethnic" neighborhoods, and when they flashed back to Homer & Marge when they lived in an apartment.

Chiiiipwich for sale! Chocolate chip or oatmeal raisin! Chiiipwich for sale!...

- Oh, and the time Homer went to New York City to get his impounded car he bought a bunch of Klauh Kalesh from a street vendor, with crab juice to wash it down.
Hoodwinked got the schnitzel truck.
Aiden Subtract works out of one of these, hawking his inventions in the Galaxy Rangers episode "Rainmaker"

Real Life

The U.S. has trucks filled with various types of food and drink that go around to any place with groups of people (construction sites, office buildings, college campuses, etc.) and sell to the people there.
- This practice is also becoming common in Britain, normally as a sideline run by a local cafe. More elaborate setups offering hotdogs, burgers etc cooked while you wait tend to be found in lay-bys, the parking lots of retail parks or dotted around pedestrianised shopping areas. They're also invariably found at markets or county fairs. Food quality ranges from unspectacular but perfectly edible to Orgasmically Delicious.
Bookmobiles, or mobile libraries as they're known in Britain.
There are companies out there that will wash your car and/or repair windshields on the spot (well in the parking lot anyway)
Ice cream trucks.
Also old-time cigarette girls.
Most of the alleged doctors in the Wild West would travel by wagon from town to town selling a 'miracle elixir' said to cure whatever ailment they could come up with. These show up in Westerns from time to time.
A close relative of this trope is the concept of the mobile MRI scanner, which is built into the trailer unit of an 18-wheeler and rotated between multiple small hospitals in rural areas.
Those Mexican ice cream men, who literally drag their store around behind them.
Japan has the yatai