Are there planets orbiting other stars beyond our solar system?
We do not know for sure,
but with the recent discoveries about 51 Pegasi, 70 Virginis and 47 Ursae Majoris
the weight of evidence is now so strong that
only a "devil's advocate" denies the conclusions.
Here is some of what we do know (this is somewhat incomplete; please see the  references below for more info):
  -  Three  small  bodies have been found  in orbit around the
      pulsar PSR 1257+12.
      They have been designated  "PSR1257+12 A, ..B, and  ..C".  
      One is about the size of the Moon, the other two
      are about 2 to 3 times the mass of Earth.
      
      They were discovered by measuring 
      variations in the pulsation speed of the pulsar which
      can be interpreted as
      gravitational effects of three small planets.
      The original observation has been confirmed but, of course, no
      direct images have been made -- that is way beyond the capabilities of
      our best telescopes.
      These planets are
      believed to have formed after the supernova that produced the pulsar.
      The present planets would have originally been within the envelope
      of the
      progenitor star and therefore
      wouldn't have stood much chance of surviving the
      supernova explosion, and wouldn't have remained in circular orbits
      after the explosion.
      Several decades of timing data on the pulsar
      PSR 0329+54 (PKS B0329+54) by
      Tatiana Shabanova (Lebedev Physics Institute)
       shows evidence of a planet with a 16.9 year
      period and mass greater than 2 Earth masses.
      But, while the evidence for these is pretty good,
      they aren't really what we're
      looking for when we talk about 'solar systems'.
  
 - 
      It has been known since 1983 that the star Beta Pictoris
      is surrounded by a disk of gas and dust.
      Spectra of Beta Pictoris show  absorption features
      which are currently believed
      to be due to cometary like clouds of gas occultating the star from the 
      debris left over from planetary formation. Though it's far from certain
      it is believed by some that planets may already have formed around
      Beta Pictoris.
      HST has
      observed Beta Pictoris (right)
      and found the disk to be significantly thinner than
      previously thought.  Estimates based on the Hubble image place the disk's
      thickness as no more than one billion miles (1600 million kilometers), or
      about 1/4 previous estimates from ground-based observations. The disk is
      tilted nearly edge-on to Earth.  Because the dust has had enough time to
      settle into a flat plane, the  disk may be older than some previous estimates. 
      A thin disk also increases the probability that comet-sized or larger bodies
      have formed through accretion in the disk.  Both conditions are believed to be
      characteristic of a hypothesized circumstellar disk around our own Sun,
      which was a necessary precursor to the planet-building phase of our Solar
      Systems, according to current theory.
      More recent HST observations
      have shown the disk to be slightly warped as might
      be expected from the gravitational influence of a planet.
      This has been confirmed by
      observations at ESO.
  
 - Recent observations at radio wavelengths of a gas cloud known as
      Bok Globule B335 have produced images of material collapsing 
      onto a newly born star (only about 150,000 years old).  
      These observations are helping to understand how 
      stars and planets form. The phenomena observed matches the theory 
      of the formation of the solar system -- that is, a large gas 
      cloud collapsed to form a star with an attendant circumstellar 
      disk in which, over time, planets accreted from the matter in the 
      disk and orbited the Sun.
  
 - The IRAS satellite found that Vega had too much 
      infrared  emission, and that has been attributed to a dust shell (with
      a mass of maybe Earth's moon).
  
 - Observations of the very nearby Barnard's Star were once thought to be
      evidence of gravitational effects of planets but they now seem to have
      been in error.
  
 - The star Gl229 seems to contain a 20 Jupiter mass
      object orbiting at a distance of 44 AU.  An object this large is probably a
      brown-dwarf rather than an ordinary planet.
  
 - 
      What may be the first discovery of a planet orbiting a normal, Sun-like 
      star other than our own has been announced by astronomers studying
      51 Pegasi,
      a spectral type G2-3 V  main-sequence star 42 light-years from Earth. At a 
      recent conference in Florence, Italy, Michel Mayor and Didier Queloz of 
      Geneva Observatory explained that they observed 51 Pegasi with a 
      high-resolution spectrograph and found that the star's line-of-sight 
      velocity changes by some 70 meters per second every 4.2 days. If this is 
      due to orbital motion, these numbers suggest that a planet lies only 7 
      million kilometers from 51 Pegasi -- much closer than
      Mercury is to the Sun 
      -- and that the planet has a mass at least half that of
      Jupiter. These 
      physical characteristics hinge on the assumption that our line of sight is 
      near the planet's orbital plane. However, other evidence suggests that this 
      is a good bet. A world merely 7 million km from a star like 51 Pegasi 
      should have a temperature of about 1,000 degrees Celsius, just short of red 
      hot. It was initially thought that it might be a solid body like a very big Mercury
      but the concensus now seems to be that it is a "hot Jupiter", a gas planet formed much farther from its star that migrated inward.
      These observations have now been confirmed by several independent observers.
      And there is some evidence for a second planet much farther out that is not
      yet confirmed.
      [ The 5.5-magnitude 51 Pegasi is easily visible in binoculars, high in the 
      evening sky, between Alpha and Beta Pegasi, the western pair of stars in 
      the Great Square of Pegasus. The star's equinox-2000 coordinates are R.A. 
      22 hours 57 minutes, Dec. +20 degrees 46 minutes. ]
  
 - On 1/17/96 Geoffrey Marcy andPaul Butler 
      announced the discovery of planets
      orbiting the stars  70 Virginis and 47 Ursae Majoris.
      70 Vir is a G5V (main sequence) star about 78 light-years from Earth;
      47 UMa is a G0V star about 44 light-years away.
      These were discovered using
      the same doppler shift technique that found the planet orbiting 51 Pegasi.
      The planet around 70 Vir orbits the star in an eccentric,
      elongated orbit every 116 days and has a mass about nine times that of
      Jupiter. Using standard formulas that balance the sunlight absorbed
      and the heat radiated, Marcy and Butler calculated the temperature of
      the planet at about 85 degrees Celsius (185 degrees Fahrenheit), cool
      enough to permit water and complex organic molecules to exist.  The star
      70 Vir is nearly identical to the Sun, though several hundred degrees
      cooler and perhaps three billion years older.
      The planet around 47 UMa was discovered after analysis of eight
      years of observations at
      Lick Observatory.
      Its period is a little over three years
      (1100 days), its mass about three times that of Jupiter, and its
      orbital radius about twice the Earth's distance from the Sun.
      This planet too probably has a region in its atmosphere where the
      temperature would allow liquid water.
  
 - As of April 1996, Drs. Marcy and Butler have discovered yet another planet
      this time around the star HR3522 (aka Rho 1 Cancri, 55 Cancri) about 45
      light years from the Earth.
      The planet is estimated to be about 0.8 Jupiter masses.
      It is likely that several more planets will show up in the initial
      set of 120 stars that they have monitored.
  
 - Several more extra-solar planets have now been discovered by
      the Butler/Marcy method.  It seems likely that there are a very large number
      of such planets out there.
  
 - Another extra-solar planet has been discovered orbiting 16 Cygni B.
      But unlike all other previously known planets this one has a very large
      orbital eccentricity (0.6); its  orbit carries it from a closest distance
      of 0.6 AU from its star to 2.7 AU.
      This calls into question many theories of planetary formation.
  
 - Detecting extra-solar planets directly is very difficult.
      Even the Hubble Space Telescope
      wouldn't be able to image planets at the expected sizes and distances
      from their suns.
 
      What HST did find were disks of matter around stars seen in 
      silhouette against the
      Orion Nebula
      (called 'proplyds', 
      for 'proto-planetary  disks' (right).
      This is great evidence for 
      how common these objects are, but the scale is way too small
      to say anything directly about planets there.
      More detailed HST images
      are now available, too.
  
 - Nevertheless, it might be possible to detect the infra-red
      radiation of very large planets
      (Jupiter-sized or more) in some circumstances.
  
 - By a stroke of good luck, HST has taken an image of what appears to be a planet
      escaping from a double star system. See the
      1998 May 28 announcement.
      If this is confirmed, the existence of extrasolar planets will be undeniable.