The crews on ISS

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There are several types of ISS crews, and the organization changed with the years.
Until 2003
The permanent crews were the main ones : they stayed in the station to maintain it and to carry out scientist experiments. They generally stayed six months in orbit and were composed of three members : two Americans and a Russian or an American and two Russians (alternatively). They were carried by shuttles (Columbia, Discovery, Atlantis or Endeavour).
There were also the « taxi-crews ». A Soyuz is permanently attached to the station to permit the permanent crew to come back on Earth in case of problem. For safety, this ship was replaced roughly every six months. The taxi-crews were made to join the station with a new ship and leave it after a few days with the old one. They were composed of three persons (maximal capacity of Soyuz).
Finally, there are crews for deliveries : supply, new segments, material, ... This crews have a variable composition and can travel with Soyuz or a shuttle.
From 2003 to 2006
On February 1st, 2003 took place Columbia's accident. NASA cancelled all shuttle's flights. Then only Soyuz was available for orbital flights and the organization changed.
Taxi-crews have been suppressed : the changes of safe Soyuz were made with the changes of permanent crews. So the new permanent crew arrived in the station with a new Soyuz, that would serve him for safety, and the previous crew left the station with the old ship.
Moreover, the size of crews has to be reduced to two members, an American and a Russian. These changes concern the crew 7 to 12.
From 2006 to 2009
Because the return of Discovery on August 9, 2005 was succesful, shuttles are used again. It permitted to have permanent crews of three persons again (since 13th crew). However, the composition didn't become exclusively American and Russian, by giving access to European astronauts (a German one arrived on July 6, 2006).
Moreover, the idea of changing the Soyuz in the same time that the crew remained. Since this change, crews are changed in two steps. Two members are replaced by two persons coming with Soyuz ; the third crew member is replaced later, generally with a shuttle.
Since 2009
The return of shuttles also permitted to build the station again (Soyuz can't carry big segments), so in 2009 its capacity raised to 6 people. Then on May 29, three astronauts joined the 19th crew and they formed together the 20th crew. This event was also the occasion to have for the first time in the station an astronaut of each five partners of ISS (Canada, ESA, Japan, Russia, USA).

So here is the list of permanent crews, adapted from the site Astrocosmos and from NASA. The dates are indicated according to international schedule GMT. For each crew, the first indicated member is the commander. Click on a photograph to enlarge it

Crew	Arrival to the station	Departure from the station	Members
Crew n°1	November 2, 2000	March 19, 2001	William M. Shepherd (USA) Iouri Pavlovich Gidzenko (Russia) Sergueï K. Krikalev (Russia)
Crew n°2	March 10, 2001	August 20, 2001	Iouri Usachev (Russia) James Voss (USA) Susan Helms (USA)
Crew n°3	August 12, 2001	December 15, 2001	Frank Culbertson (USA) Vladimir Dezhurov (Russia) Mikhaïl Tyurin (Russia)
Crew n°4	December 7, 2001	June 15, 2002	Iouri I. Onufrienko (Russia) Daniel W. Bursch (USA) Carl E. Walz (USA)
Crew n°5	June 7, 2002	December 2, 2002	Valery Korzun (Russia) Peggy Whitson (USA) Sergueï Treschev (Russia)
Crew n°6	November 25, 2002	May 3, 2003	Kenneth Bowersox (USA) Donald Pettit (USA) Nikolaï Budarin (Russia)
Crew n°7	April 28, 2003	October 27, 2003	Iouri Malenchenko (Russia) Edward Lu (USA)
Crew n°8	October 20, 2003	April 29, 2004	Michael Foale (USA) Alexander Kaleri (Russia)
Crew n°9	April 21, 2004	October 23, 2004	Gennady Padalka (Russia) Edward M. Fincke (USA)
Crew n°10	October 16, 2004	April 24, 2005	Leroy Chiao (USA) Salizhan Sharipov (Russia)
Crew n°11	April 17, 2005	October 10, 2005	Sergueï Krikalev (Russia) John Phillips (USA)
Crew n°12	October 3, 2005	April 8, 2006	William McArthur (USA) Valery Tokarev (Russia)
Crew n°13	April 1st, 2006	September 28, 2006	Panel Vinogradov (Russia) Jeffrey Williams (USA) Thomas Reiter (Germany - ESA) : arrived on July 6, 2006, also member of following crew
Crew n°14	September 20, 2006	April 19, 2007	Michael Lopez-Alegria (USA) Mikhail Tyurin (Russia) Thomas Reiter (Germany - ESA) : left on December 19, 2006, also member of previous crew Sunita Williams (USA) : arrived on December 11, 2006, also member of following crew
Crew n°15	April 9, 2007	October 19, 2007	Fyodor Yurchikhin (Russia) Oleg Kotov (Russia) Sunita Williams (USA) : left on June 20, 2007, also member of previous crew Clayton Anderson (USA) : arrived on June 10, 2007, also member of following crew
Crew n°16	October 12, 2007	April 19, 2008	Peggy Witson (USA) Yuri Malenchenko (Russia) Clayton Anderson (USA) : left on November 5, 2007, also member of previous crew Daniel M. Tani (USA) : arrived on October 25, 2007, left on February 18, 2008 Léopold Eyharts (France - ESA) : arrived on February 9, 2008, left on March 24, 2008 Garrett E. Reisman (USA) : arrived on March 12, 2008, also member of following crew
Crew n°17	April 10, 2008	October 23, 2008	Sergei Volkov (Russia) Oleg Komonenko (Russia) Garrett E. Reisman (USA) : left on June 11, 2008, also member of previous crew Gregory E. Chamitoff (USA) : arrived on June 2, 2008, also member of following crew
Crew n°18	October 14, 2008	April 7, 2009	E. Michael Fincke (USA) Yuri V. Lonchakov (Russia) Gregory E. Chamitoff (USA) : left on November 28, 2008, also member of previous crew Sandra H. Magnus (USA) : arrived on November 16, 2008, left on March 25, 2009 Koichi Wakata (Japan) : arrived on March 17, 2009, also member of following crew
Crew n°19	March 28, 2009	planned for October	Gennady I. Padalka (Russia), also member of following crew Michael R. Barratt (USA), also member of following crew Koichi Wakata (Japan) : also member of previous and following crews
Crew n°20	May 29, 2009	?	Gennady I. Padalka (Russia) : also member of previous crew Michael R. Barratt (USA) : also membre of previous crew Koichi Wakata (Japan) : left on July 28, 2009, also membre of previous crew Tim Kopra (USA) : arrived on July 17, 2009, departure planned with STS-128 Roman Romanenko (Russia) Frank de Winne (Belgium - ESA) Robert Thirsk (Canada)