A 1:150 scale paper model of a Atlantis space shuttle STS-135 measuring about 40cm tall.
Atlantis Space Shuttle Papercraft

Build your own NASA Orion spacecraft, a Multi-Purpose Crew Vehicle (MPCV) intended to carry a crew of up to 6 astronauts to destinations beyond-low Earth orbit (LEO).
NASA's Orion Papercraft via Paperinside

A very accurate and highly-detailed model of NASA's Apollo 13 LM-7 Aquarius. This papercraft from Uhu comes complete with a detailed interior as well.
Apollo 13 Lunar Module Aquarius Papercraft

A model of the NASA concept space tug, a space vehicle used to transfer payloads like satellites between low and high Earth orbits, or between Earth orbit and lunar orbit.
NASA Space Tug Papercraft

A 1:1 scaled papercraft of CleanSpace One, the first janitor satellite to be sent by École Polytechnique Fédérale de Lausanne (EPFL). The satellite was designed to clean up space debris.
CleanSpace One Papercraft

The Corona program was a series of American spy satellites operated by the Central Intelligence Agency Directorate of Science & Technology. The satellites were used for photographic surveillance of the Soviet Union (USSR), the People's Republic of China, and other areas between June 1959 and  May 1972.
Corona Spy Satellite Papercraft

The Kwangmyongsong-3 or Bright Star 3 in English, is said to be an Earth observation satellite from North Korea.
North Korean Satellite Papercraft - Kwangmyŏngsŏng-3

Kepler is a space observatory launched by NASA on 7 March 2009 to discover Earth-like planets orbiting other stars.
Kepler Space Telescope Papercraft

A full size papercraft of the Pioneer 4 spacecraft by RocketManTan. Pioneer 4 was the first U.S. probe to escape from the Earth's gravity launched on March 3, 1959.
Pioneer IV Papercraft

A 1:100000000 scaled Earth papercraft from Uhu02. This model measures about 12.7 cm in diameter. It was based on an image from NASA. Two versions are available, with and without clouds.
1/100000000 Earth Papercraft

The Vanguard 1 was the fourth artificial Earth satellite launched (March 17, 1958) and the first satellite to be solar powered. Model by RocketmanTan.

Vanguard 1 Satellite Papercraft

Curiosity is the latest Mars exploration rover which carried out the Mars Science Laboratory (MSL) mission on Mars surface. MSL was launched using Atlas V541 on 26 November 2011 and is expected to land on Mars between 6 to 20 August 2012.
Mars Rover Curiosity Papercraft

Meet the two cute Venus Climate Orbiter mascots Atsuki-kun & Kinsei-chan.
Venus Climate Orbiter Mascot Papercraft Atsuki-kun & Kinsei-chan 

Here's a nice little add-on for paper-replika's NASA Astronaut papercraft. That is a Hasselblad data camera created by Ferdinando Santandrea.

Hasselblad Space Camera Papercraft 

A lot of kids dream to become astronauts but very few get to become one. Here's another great papercraft from paper-replika. Included in the pattern are the USA and the Indonesian flags. The visor comes with 2 designs, with lunar surface reflection and mars surface reflection.

Astronaut Papercraft

There's a countdown going on for the launch of JAXA's Michibiki Quasi-Zenith Satellite System. The satellite is meant to enhance the Global Positioning System Japan. A papercraft model of the satelliteis available at the site. The antenna and the body is already available while the two remaining parts will be released on August 23.
Michibiki Quasi-Zenith Satellite System Papercraft

The model was based on Hayabusa, an unmanned space mission led by the Japan Aerospace Exploration Agency to return a sample of material from a small near-Earth asteroid named 25143 Itokawa to Earth for further analysis. In November 2005 it landed on the asteroid and attempted to collect samples but failed to do so-wiki
Hayabusa Tan Papercraft

Here's a simple Shuttle papercraft from Canon designed by Hiroshi Chiba.
Space Shuttle Papercraft

Here's a diorama depicting the Apollo 13 disaster. It was the third manned mission by NASA intended to land on the moon, but a mid-mission technical malfunction forced the lunar landing to be aborted. Its crew members were led by James A. Lovell wherein his radio transmission "Houston, we've had a problem", has become widely misquoted in popular culture as, "Houston, we have a problem".
Apollo 13 Diorama Papercraft

Here's your chance to build your own International Space Station papercraft. The International Space Station (ISS) is the largest and most complicated spacecraft ever built. It is being constructed by a collaboration of one hundred thousand people, hundreds of companies, and sixteen nations spread over four continents. This cool model is brought to you by CSIRO's Double Helix Science Club.

International Space Station Papercraft