Graphic of the Solar System as at 2003

Source: The International Astronomical Union (IAU)'s website iau.org

Solar System Exploration by Spacecrafts
(excludes Earth & Moon)

Trivia - How many "satellites" are there in Space? Answer: Thousands!? Go here and leave everything as is and click Submit. A list of thousands of spacecraft launched into space will appear. And, there are over 20,000 space junk (debris) up there around Earth's orbit.

Sun ()

Solar and Heliospheric Observatory (SOHO) (ESA) 1995-present
Solar TErrestrial RElations Observatory (STEREO)
Transition Region and Coronal Explorer (TRACE) - studies the Sun and Magnetosphere (orbiting Earth)
ACRIMSat see also Active Cavity Radiometer Irradiance Monitor (ACRIM)
Advanced Composition Explorer (ACE)
Solar-B / Hinode
Interstellar Boundary Explorer (IBEX)
Solar Dynamics Observatory (SDO)
Solar Probe Plus to be launched in 2018 to go into Sun
Helios 1 launched Nov 1978
Helios 2 launched Jan 1976
Ulysses - NASA and Ulysses - ESA (ESA and NASA) 1994-2009 see also here

Future Planned Mission
Interface Region Imaging Spectrograph (IRIS) Solar Satellite (NASA) to be launched May-June 2013

Mercury (2)

no moons
Mariner 10 (NASA) 1973-1975 | Flyby see also here
MESSENGER (MErcury Surface, Space ENvironment, GEochemistry, and Ranging) (NASA) 2004-present | Orbit

Future Planned Mission
BepiColombo - ESA's Mercury Planetary Orbiter (MPO) and JAXA's Mercury Magnetospheric Orbiter (MMO)
(ESA and JAXA) Scheduled July 2014 launch

Venus (17)

no moons
Venera 1
Mariner 2
Zond 1 see also here
Mariner 5
Venera 7
Mariner 10
Venera 9 took first photo from the surface of another world
Pioneer Venus 1 and 2
Vega 1 see also here
Vega 2
Magellan
Galileo and Galileo Legacy Site (NASA) Flyby Feb 1990 see also here
Cassini-Huygens - NASA and Cassini-Huygens - ESA (NASA, ESA, others) Flyby Apr 1998 see also here
MESSENGER (MErcury Surface, Space ENvironment, GEochemistry, and Ranging)
Venus Express (ESA) currently orbiting Venus - launched Nov 2005 - arrived Apr 2006
Venus Climate Orbiter (The Akatsuki) / Small Solar Power Sail Demonstrator (Ikaros) (JAXA) arrives 2016
Feb 13, 2012 Venus May Be Slowing Down, New ESA Data Suggests
Dec 8, 2010 Japanese probe Akatsuki misses Venus orbit

Earth

1 moon - Moon

Mars (29)

2 moons - Phobos and Deimos, both discovered by Asaph Hall in 1877
Mariner 4 (NASA) 1964-1965, 1967 | Landed 1965 see also here
Mariner 6 (NASA) 1969 | Flyby
Mariner 7 (NASA) 1969 | Flyby
Mariner 9 (NASA) 1971 | Orbit
Mars 2 (Soviet) 1971 | Orbit and the lander crash landed
Mars 3 (Soviet) 1971 | Orbit and Landed
Mars 4 (Soviet) 1973-1974 | Flyby
Mars 5 (Soviet) 1973-1974 | Orbit
Mars 7 (Soviet) 1973-1974 | Flyby
Mars 6 (Soviet) 1973-1974 | Contact lost while landing
Viking 1 (NASA) 1975-1982 | Orbit and Landed 1976 see also here
Viking 2 (NASA) 1975-1980 | Orbit and Landed 1976 see also here
Fobos 1 (Russian) 1988 Failure see also here
Fobos 2 (Russian) 1988-1989 | Only succeeded in taking photos of Mars' moon Phobos
Mars Observer (NASA) 1992-1993 Failure
Mars Pathfinder and Sojourner (NASA) 1996-1997 Pathfinder Orbit | Sojourner rover Landed
Mars Global Surveyor (NASA) 1996-2006 | Orbit
~~Nozomi (JAXA) 1998-2003 | Failure - never made it to Mars~~
Mars Climate Orbiter (NASA) 1998-1999 Failure | burned up in Mars atmostphere
Mars Polar Lander and Deep Space 2 (NASA) 1999 Failure | Crashed Landed see also here and here
2001 Mars Odyssey (NASA) 2001 - present | Orbit
Mars Express (ESA) 2003 - present and Beagle 2 (ESA) 2003 | Beagle 2 landed but lost contact
Spirit and Opportunity (NASA) 2003-2018
Spirit's mission from landing to lost contact 2004-01-03 to 2011-05-25
Opportunity's mission from landing to lost contact 2004-01-24 to 2018-06-10
Mars Reconnaissance Orbiter (MRO) (NASA) 2005 - present | Orbit 2006
Phoenix (NASA) 2007-2008 | Landed 2008
Curiosity | Mars Science Laboratory (MSL) (NASA) 2011 - present | Rover Landed 2012
MAVEN (Mars Atmospheric and Volatile EvolutioN) (NASA) 2013 - present
The ExoMars/Trace Gas Orbiter (ESA and NASA) Orbiter and lander 2016 - present
InSight (NASA) 2018 - present
Perseverance (NASA) 2020 - present

Every Mission To Mars In One Visualization 2019-04-29 Source: Jonathan Letourneau

Asteroid Belt (3)

Trivia - there are over 534,000 asteriods found.

Ceres & Vesta are the 2 largest "asteroids" in our solar system.
Dwarf planet Ceres, with an average diameter of 590 miles (950 kilometers) (Texas-sized), is also the largest body in the asteroid belt, the strip of solar system real estate between Mars and Jupiter. By comparison, protoplanet Vesta has an average diameter of 326 miles (525 kilometers), and is the second most massive body in the belt. In Dec 2014 Vesta was located 104 million miles (168 million kilometers) away from Ceres i.e. the distance between Vesta and Ceres is greater than the distance between the Earth and the sun.
Ceres is a dwarf planet that was discovered in 1801 and previously classified as a planet then an asteroid. It was the first object found in our solar system's asteroid belt.
After Dawn's visit to Vesta in 2011-2012 it has since been described as a protoplanet.
see here for more information on asteroids

Pioneer 10 (NASA) Traversed Asteroid Belt July 1972 see also here
Galileo and Galileo Legacy Site (NASA) see also here
Flyby Asteroid Gaspra Oct 1991 and Flyby Asteroid 243 Ida and it's moon Dactyl Aug 1993
Dawn (NASA) Orbited Asteroid Vesta Jul 2011 - Sep 2012 see also here
Dec 9, 2011 Is Vesta the Smallest Terrestrial Planet?

Other Asteroids
Rosetta and Philae (NASA) and Rosetta and Philae (ESA) (ESA)
Flyby Asteroid Steins Sep 2008 and Asteroid Lutetia Jul 2010
China's Chang'e-2 Makes First Asteroid Fly By Asteroid Toutatis Dec 2012

Jupiter (9)

65 known moons
In 1610 Galileo discovered 4 of Jupiter's moons - they are from nearest to farthest; Io, Europa, Ganymede and Callisto.
Three of them are the biggest moons in the solar system.
Pioneer 10 (NASA) Flyby Dec 1973 see also here
Pioneer 11 (NASA) Flyby Dec 1974 see also here
Voyager 1 (NASA) Flyby Mar 1979 see also here
Voyager 2 (NASA) Flyby Jul 1979 see also here
Ulysses - NASA and Ulysses - ESA (ESA and NASA) Flyby Feb 1991, Feb 2004 see also here
Galileo and Galileo Legacy Site (NASA) Orbit 1995 - 2003 (14 years) see also here
Also Flybys of moons: Ganymede, Callisto, Europa, Io and Amalthea. In 1995 sent Probe into Saturn
According to NASA "Galileo plunged into Jupiter's crushing atmosphere on Sept. 21, 2003. The spacecraft was
deliberately destroyed to protect one of its own discoveries - a possible ocean beneath the icy crust of the moon
Europa."
Cassini-Huygens - NASA and Cassini-Huygens - ESA (NASA, ESA, others) Flyby Dec 2000 see also here
New Horizons (NASA) Flyby Feb 2007 see also here and here
Juno (NASA) Launched Aug 2011 | Arrives July 2016 see also here
Apr 4, 2012 Outer-Planet Moons Found — and Lost
Mar 1, 2012 Europa's Ocean May Be Too Acidic for Life
Jul 24, 2009 Hubble reawakens, snaps image of Jupiter scar
Jul 21, 2009 Mystery impact leaves Earth-size mark on Jupiter

Centaurs (minor planets)

These are small Solar System bodies that orbits the Sun between Jupiter and Neptune and crosses the orbits of one or more of the giant planets. It has been estimated that there are around 44,000 centaurs in the Solar System with diameters larger than 1 km. more about Centaurs here

Centaur (10199) Chariklo - First Ring System Around Asteroid and Fifth Ring System in Solar System (after gas giants)

Saturn (4)

62 known moons - largest moon is Titan, moon Enceladus has ice
Pioneer 11 (NASA) Flyby Sep 1979 see also here
Voyager 1 (NASA) Flyby Nov 1980 see also here
Voyager 2 (NASA) Flyby Aug 1981 see also here
Cassini-Huygens - NASA and Cassini-Huygens - ESA (NASA, ESA, others) Orbit Jul 2004 - present see also here
Huygens landed on Titan in Jan 2005 and still active
Also flybys of moons: Phoebe and Titan
Apr 4, 2012 Outer-Planet Moons Found — and Lost

What You Don't Know About Saturn discovered in 1979
NASA - Cassini Images Bizarre Hexagon on Saturn's North Pole
Giant hexagon of clouds spins on Saturn while clouds disappear from Jupiter

Uranus (1)

27 known moons
Voyager 2 (NASA) Flyby Jan 1986 see also here
Dec 23, 2005 Hubble finds new moons, rings around Uranus

Neptune (1)

13 known moons
Voyager 2 (NASA) Flyby Aug 1989 see also here
Oct 18, 2010 First asteroid in Neptune's trailing Trojan zone discovered - New Horizons perhaps may investigate

Dwarf Planets (6 + 4) (classified in 2006) see Mike Brown's Planets

Ceres (1) (discovered in 1801 and previously classified as a planet then an asteroid)
SEE ASTEROID BELT FOR MORE INFO
Dawn (NASA) see also here
Mar 6, 2015 Spacecraft becomes first to orbit mysterious dwarf planet Ceres - CNN
Mar 6, 2015 Dawn spacecraft starts to orbit Ceres in mission to photograph dwarf planet - The Guardian
Mar 6, 2015 NASA Probe Finally Arrives at an Icy Alien World - Wired

Pluto (1) (previously classified as a planet, called 9th Planet for decades) | a Trans-Neptunian Object (TNO)
5 known moons (Charon, Nix, Hydra, Styx, Kerberos)
New Horizons (NASA) see also here and here Pluto Closest Approach Jul 2015, then Charon | Launched Jan 2006
Jul 12, 2012 Hubble Discovers a Fifth Moon Orbiting Pluto
Jul 11, 2012 Hubble telescope spots fifth moon near Pluto
Sep 5, 2011 Dwarf Planet Mysteries Beckon to New Horizons
Jul 20, 2011 Tiny fourth moon discovered in Pluto's orbit
Oct 31, 2011 Pluto — No Longer a Planet — Has a Twin Sister
Oct 18, 2010 Reaching the Mid-Mission Milestone on the Way to Pluto

Eris (formerly 2003 UB313 and/or Xena, called 10th Planet by NASA for almost a year)
a Trans-Neptunian Object (TNO)
1 known moon (Dysnomia)
NIL
Oct 26, 2011 Faraway Eris Is Pluto's Twin
Oct 21, 2011 Pluto — No Longer a Planet — Has a Twin Sister
Oct 10, 2010 Nitrogen, Methane Dominate Icy Surface of Eris

Haumea (formerly 2003 EL61 discovered Dec 28, 2004) | a Trans-Neptunian Object (TNO)
2 known moons (Namaka, Hi'iaka)
NIL

Makemake (discovered in Mar 2005) | a Trans-Neptunian Object (TNO)
no known moons
NIL
Nov 22, 2012 Dwarf planet Makemake lacks atmosphere

See also Oort Cloud

The following may be grouped in by some but is not recognized by the International Astronomical Union (IAU) as dwarf planets:
Orcus (discovered 2003) | a Trans-Neptunian Object (TNO)
1 known moon (Vanth)
NIL
Snow White (formerly 2007 OR10) | a Trans-Neptunian Object (TNO)
NIL
Quaoar (discovered in June 2002) | a Trans-Neptunian Object (TNO)
1 known moon (Weywot)
NIL

The Kuiper Belt (1) ~30-50AU (also called the Edgeworth-Kuiper Belt and the Trans-Neptunian Belt)
the massive band of comet-like bodies that circles the solar system

The Kuiper Belt, a region of the outer solar system extending past Neptune, contains small or "dwarf" planets; these are icy objects of a variety of sizes up to thousands of kilometers across. The first KBO other than Pluto was only discovered in 1992, and the KBO population is still not well mapped.

New Horizons see also here The Kuiper Belt (2016-2020)

Aug 29, 2012 The Kuiper Belt at 20: Paradigm Changes in Our Knowledge of the Solar System

Oort cloud beyond 50AU - a vast region of space that may be where many comets come from

Sedna - a dwarf planet not recognized by the IAU (discovered Nov 14, 2003) | 76AU away
Mar 16, 2004 Scientists: Most distant object in solar system found

2012 VP113 - a dwarf planet (discovered 2012) | 80AU away
Mar 27, 2014 A planet past Pluto? Astronomers redefine the solar system's edge
Mar 27, 2014 Super-earths beyond Pluto? New discovery hints they might exist
Mar 27, 2014 Astronomers discover new dwarf planet and possible super-Earth in our Solar System
Mar 27, 2014 Astronomers dub new dwarf planet 'Biden.' Will the name stick?
Mar 27, 2014 Dwarf planet discovered at solar system's edge
Mar 26, 2014 New Solar System Dwarf Planet Discovered and Solar System's Edge Redefined
Mar 26, 2014 Astronomers find mini-planet in solar system's backyard

Comets (Trivia - there are over 3000 comets found)
- believed by some to come from the Kuiper Belt and by others the hypothesized Oort cloud
see here for more information on comets
SOHO, launched Dec 1995, has found more comets than any other spacecraft, or person, to date. The mission logged its 2,000th comet discovery in December 2010.

Galileo and Galileo Legacy Site (NASA) see also here
Comet Shoemaker-Levy 9 Impact Observations in July 1994
Ulysses - NASA and Ulysses - ESA (ESA and NASA) see also here
Comet Hyakutake Encounter May 1996
Halley's Comet - visited by Vega 1 & 2, Suisei, Sakigake and Giotto and studied by Pioneer 7 and Pioneer Venus 1 in 1986
Chiron (discovered in Nov 1977)
Rosetta and Philae (NASA) and Rosetta and Philae (ESA) (ESA)
Comet 67P/Churyumov-Gerasimenko arrival May 2014 - Rosetta to orbit and Philae to land

Planet X

Heliosphere 75-90AU to ~230AU (a protective bubble that shields and protects our solar system / border of Solar system)
(Local Interstellar Cloud)
Pioneer 10 and 11 (mission ended 1995 & 1997 respectively)
Voyager 1 and 2 both were launched in 1977
Interstellar Boundary Explorer (IBEX) see also here orbiting Earth
Jan 31, 2012 IBEX reveals the unexpected "atmosphere" that surrounds our entire solar system

Heliopause

Interstellar Medium (space between stars)

Solar System Exploration by Spacecrafts (excludes Earth & Moon)