The best portal to information about deep-space planetary-exploration probes is the Lunar and Planetary Science site at the NASA National Space Science Data Center (NSSDC). One can often find more detailed information in this site than in the official mission home pages we list below. And not just for the pre-WWW missions!
To the Moon:
The Soviet Union's lunar program: Luna (1-24) and Zond (3-8) (1959-1976).
The heroic age of NASA, part 1: Apollo 8, 10, 11, 12, 14, 15, 16, 17 (1968-1972).
JAXA's (Japan's) first moon shot: Hiten (1993).
ESA's (Europe's) first moon shot: SMART-1 (2003-2006).
Brand new: JAXA'a Kaguya/SELENE, launched 14 September 2007.
NASA's Mariner 10 (1973-1975).
NASA's MESSENGER (launched 2004, to arrive 2011).
Coming "soon": ESA's Bepi-Colombo will be launched in 2013 and arrive in 2019.
NASA's Magellan (1990-1994).
ESA's Venus Express (2005-2007).
Venus is often visited by satellites on their way to somewhere else, in order to pick up a gravity boost from the planet. Prominent among these flybys have been the NASA Mercury missions, and the Galileo and Cassini missions to Jupiter and Saturn.
The beginning of the good stuff: NASA's Viking 1 and Viking 2, each with an orbiter and a lander (1975-1982).
The real beginning of the Martian spacecraft curse: the Soviet Union's ill-fated Phobos 1 and Phobos 2 (1988-1989).
The curse hits in earnest: NASA's Mars Observer (1992-1993), RSA's (Russia's) Mars 96 (1996), NASA's Mars Climate Orbiter (1998-1999), Mars Polar Lander and Deep Space 2 probes (1999), ISAS's (now called JAXA's) Nozomi (1998-1999), and the Beagle 2 lander carried and deployed by ESA's Mars Express (2003), all failed. Several of these were good examples of the "faster-better-cheaper" spacecraft-development philosophy.
NASA's Mars Global Surveyor (1996-2006), on the other hand, lasted four times as long as expected before succumbing to battery failure.
Introducing the Martian rover: NASA's Mars Pathfinder (1996).
Wrong planet for the metaphor, but: NASA's 2001 Mars Odyssey still works fine (2001- ).
ESA's Mars Express orbiter still works, despite the demise of Beagle 2 (2003- ).
Even cuter and more durable than Pathfinder: NASA's Mars Exploration Rovers, Spirit and Opportunity (2003- ).
NASA's Mars Reconnaissance Observer is doing well too (2005- ).
Brand new: the U.Az./NASA Phoenix mission, launched 4 August 2007, will attempt again to land near the Martian north pole. As its name suggests, this mission has risen from the ashes of Mars Polar Lander and Deep Space 2.
Lots more to come: launches are planned for the approach to every Martian conjunction (every 26 months).
To the asteroids:
NASA's Shoemaker (formerly NEAR) (1996-2001).
NASA's Deep Space 1 (1998-2001).
JAXA's Hayabusa (launch 2003, rendezvous 2005, return to Earth 2010).
ESA's Rosetta (launch 2004, rendezvous in 2008, 2010 and 2014) will place a lander on one of the three asteroids it will visit.
Asteroids are sometimes seen at close range by satellites on their way somewhere else, notably the NASA missions Galileo, Cassini, and Stardust.
To the outer planets:
The heroic age of NASA, part 2: Voyager 1 and Voyager 2 (1977- ). This mission rivals the Apollo program in the magnitude of the advance it has contributed to our civilization, and it has been much cheaper, even though it's been going for 30 years already.
Still under construction!