Agency

SLC-6, aka "Slick 6", was the planned shuttle launch pad at Vandenberg AFB. It was never used, but much integration work was performed in anticipation of a launch there. 

Unknown function

Air Force Flight Test Center  (AFFTC) provides contingency support for shuttle landings at Edwards AFB.

The "Apollo 14" embroidery in this patch extends the entire height of the border area and the letter spacing is odd. The moon is grayscale.

Astrotech Corporation, formerly Spacehab Inc., is an aerospace company headquartered in Austin, Texas which provides commercial space products and services to NASA, the U.S. Department of Defense, international space agencies, and global commercial customers. The Company changed its name to Astrotech Corporation in 2009 to align the corporate name with the company's core business offering, Astrotech Space Operation. Astrotech Space Operations provides all support necessary for government and commercial customers to successfully process their satellite hardware for launch, including planning; construction and use of unique equipment and facilities; and spacecraft checkout, encapsulation, fueling, and transport. In its 29 year history, Astrotech has supported the processing of more than 290 spacecraft without impacting a customer’s launch schedule.

Apollo 14 team member patch.

This is a modern reproduction of the original Apollo 11 Lunar Team patch. There are minor differences in the letter stitching and embroidery styles. 

The Association of Space Explorers is a non-profit organization with a membership composed of people who have completed at least one Earth orbit in space (as defined by the Fédération Aéronautique Internationale). It was founded in 1985, and the current membership stands at 320 from 34 different countries. The organization provides a forum for the promotion of space exploration, as well as space science and engineering and environmental awareness.

Designed by Alexei Leonov.

The Guiana Space Centre or, more commonly, Centre Spatial Guyanais (CSG) is a French and European spaceport near Kourou in French Guiana. Operational since 1968, it is particularly suitable as a location for a spaceport as it fulfills the two major geographical requirements of such a site:
it is quite close to the equator, so that the spinning earth can impart some extra velocity to the rockets for free when launched eastward, and
it has uninhabited territory (in this case, open sea) to the east, so that lower stages of rockets and debris from launch failures cannot fall on human habitations.
The European Space Agency, the French space agency CNES, and the commercial Arianespace company conduct launches from Kourou. This is the spaceport used by the ESA to send supplies to the International Space Station using the Automated Transfer Vehicle.

Galileo was an unmanned NASA spacecraft which studied the planet Jupiter and its moons, as well as several other solar system bodies. Named after Renaissance astronomer Galileo Galilei, it consisted of an orbiter and entry probe. It was launched on October 18, 1989, carried by Space Shuttle Atlantis on the STS-34 mission. Galileo arrived at Jupiter on December 7, 1995, after gravitational assist flybys of Venus and Earth, and became the first spacecraft to orbit Jupiter. It launched the first probe into Jupiter, directly measuring its atmosphere. Despite suffering major antenna problems, Galileo achieved the first asteroid flyby, of 951 Gaspra, and discovered the first asteroid moon, Dactyl, around 243 Ida.

There appear to be several versions of this patch, including a gray-bordered version and a version without the star cluster on the left.

Johnson Space Center TV

Air Force Plant 42 (AFP 42) is a federally owned military aerospace facility under the control of the Air Force Material Command (AFMC) in Palmdale, California. Aerospace contractors at Air Force Plant 42 share a common runway complex and either lease building space from the Air Force (commonly referred to as GOCO, or Government Owned Contractor Operated), or own their own building outright. There are eight separate production sites specially suited for advanced technology and/or "black" program projects. Currently the most well–known contractors at Plant 42 are Boeing, Lockheed Martin (home of the legendary Skunk Works), and Northrop Grumman. Plant 42 as of August 2010 has updated their operation status from GOCO (Government Owned Contractor Operated) to a DoD operated facility. Privately–run since 1954, the Air Force under the Obama administration chose to insource the contracted operations of the plant. Now it is run by DoD resources, with Detachment 1 in command.

The John F. Kennedy Space Center (KSC) is the United States launch site that has been used for every NASA human space flight since 1968. Although such flights are currently on hiatus, KSC continues to manage and operate unmanned rocket launch facilities for the U.S. government's civilian space program from three pads at the adjoining Cape Canaveral Air Force Station. Its Vehicle Assembly Building (VAB) is the fourth-largest structure in the world by volume and was the largest when completed in 1965.

The Okinawa Tracking and Communication Station was established in February 1968 as the Okinawa Radiowave Tracking Base of the then Science and Technology Agency (STA) Space Development Headquarters, which was affiliated with the then National Space Development Agency (NASDA) as its facility when NASDA was established in October 1969. In October 2003, the Japan Aerospace Exploration Agency (JAXA) was established, and the station became a JAXA facility.
The main role of the Station is to track and control satellites. It plays a role to maintain and control satellites by receiving radio waves from satellites in space to confirm their positions and attitudes and to learn if their onboard electronic devices are functioning properly. If necessary, command signals are also transmitted from the station to satellites.

The Okinawa Tracking and Communication Station was established in February 1968 as the Okinawa Radiowave Tracking Base of the then Science and Technology Agency (STA) Space Development Headquarters, which was affiliated with the then National Space Development Agency (NASDA) as its facility when NASDA was established in October 1969. In October 2003, the Japan Aerospace Exploration Agency (JAXA) was established, and the station became a JAXA facility.
The main role of the Station is to track and control satellites. It plays a role to maintain and control satellites by receiving radio waves from satellites in space to confirm their positions and attitudes and to learn if their onboard electronic devices are functioning properly. If necessary, command signals are also transmitted from the station to satellites.

NASA - Kennedy Space Center

DOD Manned Space Flight Support Office or DDMS
 

Marshall Spaceflight Center (MSC) Security

John C. Stennis Space Center (SSC)

Team NASA - Johnson Space Center

The official NASA patch for the Shuttle-Mir Program, showing a Space Shuttle Orbiter docked to the Russian Space Station Mir, flying above a stylised Earth. The patch is bordered by the colours of the flags of Russia and the USA

Johnson Space Center Logistics Division

Unknown purpose

Cape Canaveral Air Force Station (CCAFS)
 

The Energy Systems Division is responsible for providing engineering expertise for human and human supported spacecraft in the areas of propulsion systems, fluid systems, pyrotechnics, power generation, and power distribution and control systems. Additionally, the division operates and maintains facilities for testing of hardware within these areas of expertise. The division provides conceptual design, feasibility studies, analysis, development, qualification testing, flight certification, operations, and sustaining engineering. The division also pursues technology and development of new concepts for implementation in these areas of expertise.

Team Nasa - Stennis Space Center

This is the company that builds and supports SpaceHab, the Neutral Bouyancy Lab and Space Vehicle Mockup Facility.

International Cospas-Sarsat Programme is a satellite-based search and rescue (SAR) distress alert detection and information distribution system, established by Canada, France, the United States, and the former Soviet Union in 1979. It is best known as the system that detects and locates emergency beacons activated by aircraft, ships and backcountry hikers in distress. Over the years many countries have joined the project, either as providers of ground segments or as user states. As of 2011, 26 countries (Algeria, Argentina, Australia, Brazil, Chile, People's Republic of China, Greece, India, Indonesia, Italy, Japan, Republic of Korea, New Zealand, Nigeria, Norway, Pakistan, Peru, Saudi Arabia, Singapore, South Africa, Spain, Thailand, Turkey, United Arab Emirates, United Kingdom, Vietnam) and two organizations (Chunghwa Telecom of Chinese Taipei and the Hong Kong Marine Department) are providers of ground segments, while 11 countries are user states (Cyprus, Denmark, Finland, Germany, Madagascar, Netherlands, Poland, Serbia, Sweden, Switzerland, Tunisia).[1] Cospas-Sarsat is based in Montréal, Québec, Canada, and is headed by Steven Lett of the United States.
COSPAS (КОСПАС) is an acronym for the Russian words "Cosmicheskaya Sistema Poiska Avariynyh Sudov" (Космическая Система Поиска Аварийных Судов), which translates to "Space System for the Search of Vessels in Distress". SARSAT is an acronym for Search And Rescue Satellite-Aided Tracking.