Space Mountain had its official opening on May 27, 1977. Although the coaster was originally designed in the late 1960s (just after Walt Disney's death), ride control systems at that time were not sophisticated enough for WED's plans. Disneyland's Space Mountain was the second to be built, after Walt Disney World's opening in 1975. Space Mountain is one of the few rides that appears at each of the Disney resorts worldwide.
Disney Quest is already open, and has been for a while... if you mean when did it open I have no idea, and if you mean the time it is open I am pretty sure it opens whenever Downtown Disney does.
The official opening date is May 20, 2011, although it will most likely be open during the days before for a "soft opening".
Star Tours was created in 1986.
Evil Star was created in 1948.
The Star Spangles was created in 2001.
Malvern Star was created in 1902.
Death Is a Star was created in 1982.
Star Dates was created in 2002.
Star Tours ended in 2012.
Parliament of Tours was created in 1589.
Cannibal Tours was created in 1988.
Toyland Tours was created in 1994.
Tours Aillaud was created in 1976.
Tours FC was created in 1919.
RocketShip Tours was created in 2008.
Transocean Tours was created in 1957.
Caravan Tours was created in 1952.
Carica-Tours was created on 1952-09-12.
Akbar's Adventure Tours was created in 1998.
Joué-lès-Tours FCT was created in 2008.