Space Plane

In essence, a spaceship that can take off and land like an aircraft, as well as looking like an aircraft. Many ships have Vertical Take Off Or Landing capabilities, these babies though can use a regular runway too.

Saves you the cost of a space launcher that you only use once. The obvious technical issue is that you need a store of liquid oxygen on board for the actual space bit of the journey- as you need something to burn the hydrogen with once the air gets too thin. Another issue is the ability to get to Mach 25, but that's not too hard.

Please note that this excludes:

the Space Shuttle, which requires two boosters, a launch pad and a huge fuel tank to get into orbit. It is also incapable of any real powered flight, having to glide back to Earth. It pretty much defines the term 'Flying Brick'.
Buran, the Soviet equivalent, which used a single powerful rocket to get into orbit, rather than relying on its own power.
Craft such as X-15 and SpaceShipOne that require another aircraft to get them to a launching height.
The X-37, which is launched by an Atlas V 501. It doesn't carry nearly enough fuel—fully loaded, it masses just under 5 metric tons. Compare with the Space Shuttle, which masses 2,000.

The spaceplane must be single-stage-to-orbit or sub-orbit to qualify. Nobody's built one, as of June 2011.

Usually an example of the Cool Plane. See also: Space Fighter.

Examples of Space Plane include:

Anime & Manga

The Gekko-Go of Eureka Seven is a large aircraft that is capable of entering low orbit for quick trans-globe travel.
The Macross franchise is the king of this trope, featuring space planes that are also Transforming Mecha—but, perhaps surprisingly, they end up spending more time in plane form than mecha form. The earlier models of variable fighters generally required a lift from another craft to reach space but by the time of Project Supernova they're capable of reaching orbit from planetary surfaces, even loaded down with an optional extra fold booster.
- Alto and Michel demonstrate the same again when escaping from Gallia IV
In Mobile Suit Gundam, the FF-3/FF-S3 Sword Fish is a multi-use interceptor that functions in high altitude and low orbit. It's successor, the Transformable Humongous Mecha MSZ-006C4 Zeta plus C4 is a Humongous Mecha version of it, and its Super Prototype, the MSZ-006 Zeta Gundam is basically the real Space Plane version for both full range aerial and space combat, instead of only specializing in around the atmosphere.

Film

X-15 (1961). A movie starring Charles Bronson as the pilot of the world's first spaceplane. Apparently has a dull plot mixed with good Stock Footage of the eponymous X-15.
The Colonial Marines' dropships in Aliens.
The various shuttlecraft of Star Trek, though whether they meet the definition of this trope might be a matter of opinion; the original shuttle met the single - stage to orbit, rocket rather than antigravity power, and aerodynamic shape requirements.
As mentioned in the "Literature" section, most Star Wars space - capable vehicles smaller than about 200 meters are able to land on planets, but this is due to repulsorlift engines rather than conventional aircraft design. The shape of Naboo space fighters and space yachts, however, appear very similar to jet aircraft.
In Starship Troopers, dropships pick up the title characters. It's not clear how they get from surface to space, but they do look and act like a Space Plane.
One of the purest examples of this trope is the "Orion III" Space Plane model, which appeared briefly in 2001: A Space Odyssey.
The Valkyrie shuttles from Avatar.
Justified in Lilo and Stitch where Jumba's spaceship is actually based on the very passenger jet he, Pleakley, Nani, and Stitch were going to steal and use it to rescue Lilo from Gantu, which was changed due to the 9/11 terrorist attacks.
Commercial airliners are capable of interstellar flight in The Fifth Element.

Literature

The Duumvirate's fusion-powered jet can take them to Mars without a booster.
The Black Stallions from the novel of Dale Brown. They can go to orbit, as the first usage of one in Strike Force shows, but sub-orbital is enough most of the time.
X Wing Series X-Wings and Y-Wings don't typically count; they have repulsorlift coils and use them. But Starfighters of Adumar has a pilot recount the case of another pilot whose craft had been shot up so the repulsorlifts had stopped working, and who had instead approached the cleared landing zone on the local moonbase, dropping his skids as he got close. Wes can tell the story.

Wes Janson: "The skids take the initial impact but he bounces, so he's like some sort of hop-and-grab insect all down the duracrete. But he's lucky enough that he stays top side up. Finally he's bled off a lot of momentum, but he loses control and his Y-Wing rolls. Comes to a stop on its belly and he's safe. Then his ejector seat malfunctions and shoots him off towards space. With grav that low, he achieves escape velocity. We had to send a rescue shuttle up after him or he'd still be sailing through the void, one cold cadaver."

The book Gradisil by Adam Roberts features jet planes being retrofitted to journey into Low Earth Orbit. By riding on electromagnetic fields the planes, over the course of a day or so, can reach orbit. Big planes like a 747 are used to lift private space-habitats into orbit.
Fluggers in Tomorrow War series by Alexander Zorich are like this. While obviously VTOL-capable, they rely on mobility to survive, so generally act plane-like and actually fly in atmosphere rather than just lift and descend. At the start of the first book one corporation tried to have shields and stable atmospheric flight at the same time - this took them some time.

Live Action TV

Battlestar Galactica's Colonial Vipers and Cylon Raiders could fly and fight both in an atmosphere and in a vacuum.
- Both might fail on technicalities. If a "spaceplane" has to "take off and land like an airplane," well, how Vipers would land at a ground-based facility—or take off again, on those skids—is never established. And do Raiders even have landing gear? (This doesn't mean that appropriate facilities don't exist or couldn't be built; it's just that, if they were, we never saw 'em. Both types of craft always launched from and and returned to a starship, which is not "like an airplane.")
- We do actually see Mk VII Vipers being towed around an airbase in the new Battlestar Galactica, in a flashback set just after the death of Zack Adama. That sequence, plus some close-ups in Galactica's hangar deck seem to indicate that the skids have some retractable(?) wheels which could be used for a conventional runway take-off and landing. The Raptor, however, would probably count as a single-stage VTOL spaceplane.
In Stargate, Goa'uld gliders, human X-302s, and Wraith darts can fly in space and in atmosphere
Red Dwarf had several Starbugs and Blue Midgets. Starbug is explicitly stated to be a ship-to-surface craft, implying that it ferried ore from the surface of the planet or asteroid it was mining to the ship itself. Neither of those fly like planes, however.
The Doctor Who episode "Victory of the Daleks" has Dalek technology co-opted by Britain during World War II to produce Space Spitfires.
- The "Doctor Who" episode "When a Good Man Goes to War" has the exact same Spitfires returning to help The Doctor take control of a space station called Demons Run.
One turns up, in of all places, CSI: Miami.

Tabletop Games

In BattleTech, there are Aerospace fighters which can act as normal fighter aircraft or fighter aircraft In Space at the discretion of the mothership, at least some of which are capable of surface - to - space flight, winged shuttlecraft, and Aerodyne Dropships, which are able to land as a Space Plane.
In Warhammer 40,000, the Imperial Navy's aircraft - by which I mean fighters and bombers designed primarily to operate in an atmosphere - are technically spaceplanes, as they can be launched off an Imperial Navy starship in orbit and can reach that starship from ground airbases once the fighting's over. In something of a subversion, the Imperial Navy's starfighters - like the Fury - are altogether much larger than standard aircraft and have a crew of around three, and while they can operate in an atmosphere it's not recommended because they're not designed for it.
Many small craft and even Starships in Traveller are capable of this. Not all, particularly the biggest which is why the largest starports tend to have orbital facilities.

Video Games

The Delta-glider Mk.4 (and many other cool spaceplanes) from Orbiter. It can do an Earth to Moon and Earth to Mars journey easily.
- The XR series (XR1 is a just a more sophisticated Delta-glider)
  - The XR2 Ravenstar is probably one of the more awesome examples from orbiter, as its basically a Space capable reimagining of the SR-71 Blackbird, and has the gloriously powerful engines to match.
Freelancer space ships seem fully capable of launching and landing, though gameplay always uses docking rings, presumably for traffic control.
Battlecruiser 3000 AD shuttles are capable of atmosphere to space and back.
Starting with Wing Commander III, some fighters are explicitly said to be capable of flying and fighting in an atmosphere, while others aren't.
Civilization: Call to Power has several units that can launch themselves into space. (Including an actual Space Plane unit, and a unit called a Space Fighter). The Civilization 2: Test of Time Sci-fi game also has several units that can travel into space. (The Shuttle is probably the most obvious example.)
Several ships in the Mass Effect universe - the Normandy SR1 can fly in atmosphere, the Kodiak Drop Shuttle and the Viper gunship can both transit too, as can starfighters.
In Final Fantasy VIII, you get one of those in place of a Global Airship. It's called Ragnarok.

Western Animation

An American educational series involving robots visiting other planets. Help with the show name would be appreciated.
An inversion is the Turbokat, which is a jet that can go into space if necessary.
All E-frame from Exo Squad seem to have direct-atmosphere-to-space-and-back capability, but most of them fall under Humongous Mecha, so only Kaz Takagi's CR-001 Exofighter qualifies for the "plane" part.
The Disney show Chip and Dale: Rescue Rangers had an episode, imaginatively called "Space Plane" which revolved around Chip and Dale getting trapped in a space plane, forcing Gadget to cook up a scheme involving a homemade spaceship with fire extinguisher thrusters, dynamite-powered rockets, all powered by pulling cables with nuts and washers attached to them.

Real Life

Sort of - none of these have really got off the ground yet.

The Silbervogel design from Nazi Germany.
The British HOTOL (Horizontal Take Off Or Landing) project, cancelled in 1988 after development problems.
The European Space Agency Skylon project, pictured above.
X-30 "National Aerospace Plane", which was never built. A smaller version, the X-43, reached a maximum speed of nearly Mach 10 using a Pegasus missile as a booster. Keep in mind that to be a true Space Plane, an aircraft would need to reach somewhere around Mach 25, depending on what altitude you were at, without a booster.
The XCOR Lynx rocketplane. It will only be able to reach Mach 2 or 3, however, and will be limited to brief, sub-orbital spaceflight only.
There are several proposed designs which use a magnetic launch system to achieve the necessary launch velocity. Naturally none have been built due to cost; it could also be argued that any craft launched by such a system would not be a true space-plane, since it wouldn't be taking off under its own power.
The Hypersoar was a commercial airliner project that would fly to the edge of space and skip across the atmosphere, making it extremely fast and thrifty with fuel while avoiding the Concorde's noise problems. It was quickly shelved when it was realized the skipping effect couldn't be done effectively without repeated +1G/-1G shifts in acceleration.