Mission Name Launch Description
Deep Space 1
NASA
(updated URL)
1998 Deep Space 1 flew within 10 miles of asteroid 1992 KD (Braille) on July 28, 1999. (The mission is mainly a test of new propulsion and navigation technology)
DS1 Mission Log - for the latest news in a chatty style by Dr Marc Rayman. Now on its way to Comet Borelly.
NEAR
NASA
1996 Flyby within 753 miles of Asteroid Mathilde in June 1997. Earth swingby January 1998. Planned Eros rendezvous in January 1999 failed. Next attempt 14 February 2000. NEAR will go into orbit around Eros.
Clementine II
DoD (no official web links but see Time report)
1998 - scrapped Rendezvous with asteroid Toutatis. Fire rocket at surface and observe ejected material. A way of checking the asteroid's composition and mechanical strength. Mission cancelled by Pres Clinton in October 1997.
LUNAR-A
Japanese Space Agency
1997? LUNAR-A to the Moon is carrying and  shooting three penetrators on the lunar surface. The penetrators will conduct lunar seismometry and several measurements of surface thermal properties to know much better about interrior structure of the moon. A by-product might be the detection of meteoroid impacts, as was done with the Apollo missions
CONTOUR
NASA/JPL
2002 After being launched in August 2002, the CONTOUR spacecraft will study three diverse comets, Encke, Schwassmann-Wachmann 3 (SW3), and d'Arrest. Using multiple Earth swingby maneuvers to reshape its trajectory, the CONTOUR spacecraft will conduct flyby encounters with comets Encke, SW3 and d'Arrest in 
November 2003, June 2006, and August 2008 respectively.
Rosetta
ESA (European Space Agency)
Jan 2003 Designed to land, and stay on, comet Wirtanen as it tours the inner solar system.
Stardust 
NASA
1999 (on its way) Will fly past comet Wild-2 and capture dust grains blown from the comet's surface
NEAP Spacedev Corp Apr 2001 SpaceDev is a publicly owned company. With the assistance of the science community, SpaceDev has selected 4660 Nereus, possibly a carbonaceous near earth asteroid, as its NEAP mission target. To reach Nereus, NEAP is currently scheduled to 
launch on April 3, 2001 (possibly put back 9 months to simplify the mission) 
NEAP will be the first to land payloads on the surface of an asteroid.
Space Technology4/Champollion
NASA/JPL
Cancelled
(was 2006)
Space Technology 4/Champollion will be 
sent to the comet Tempel 1 to test advanced technology. Attempting a feat never done before, ST4/Champollion will actually land on the comet's nucleus after surveying and mapping it for several months. It will take photographs of its surroundings, drill for material below the surface of the nucleus, and perform scientific experiments. 
Update: Due to budgetary constraints, the Space Technology 4 mission was cancelled on July 1, 1999.
Deep Impact
NASA/University of Maryland
2005 A University of Maryland proposed space mission to 
penetrate deep into the nucleus of a comet. The launch of the Deep Impact mission is planned for January 2004. The schedule calls for the mission to reach its target, comet Tempel 1, at the beginning of July, 2005 with impact on July 4.
CRAF NASA 1995 - scrapped The main target of the CRAF mission was Comet Kopff. On its way to the comet, an asteroid flyby of Hamburga was to be executed.
HERA
University of Arkansas
2006? Proposed Discovery mission. See Space.com item. The spacecraft would first reach asteroid A 010 seven months later and spend 99 days hovering above the space rock.After that, Hera will change course and fly to asteroid 2000 AG 6. It is to arrive there in November 2006 and stay for 98 days. Then Hera will fly to asteroid 1989 UQ in March 2009 and stay there for 205 days. Finally, it will head back in the vicinity of Earth where it will jettison a small capsule into the atmosphere. That capsule will parachute to a landing on Earth in November 2010.
 HAYABUSA (Muses-C)
Japan's Institute of Space and Astronautical Science
Mid 2005
Asteroid "Itokawa" - sample return. In Wake Of Stardust Comet Flyby, Hayabusa Aims For Asteroid Sample Return