The orbital ellipticities are best viewed graphically.
The occurrence of circular orbits may require
special initial conditions, to avoid the gravitational perturbations and
to avoid the tendency of the 2nd Law of Thermodynamics to scramble the
orbital ellipticities of planets. Perhaps, our Solar System, with its coplanar,
nearly circular orbits represents a remarkably fortuitous low-entropy state
for a planetary system.
Rasio and Ford 1996, Science, vol 274, 954. Weidenschilling and Marzari, 1996, Nature, v384, p619) Lin and Ida 1997
Holman, Touma, Tremaine 1997, submitted to Nature Mazeh et al. 1997
G.Laughlin and F.Adams: Astrophysical Journal Letters, vol 508, p.L171
Artymowicz 1992, PASP, 104, 769 Lubow and Artymowicz 1996 (see their Web presentation) Cassen 1995
The circular orbit of Jupiter in our Solar System promotes the stability of circular orbits among the other 8 planets. If our Jupiter were in an eccentric orbit, the Earth and Mars would likely be gravitationally scattered out of the Solar System. Thus our existence, and the existence of life in the habitable zone, depends on both Jupiter and Earth being in mutually stable, circular orbits. It is probably no accident that our Solar System contains circular orbits.
Eccentric orbits may occur relatively commonly for extrasolar planets. Just one eccentric giant planet orbiting a star can spell dynamical doom for terrestrial planets, and may bode ill for slowly evolving creatures. The claim that all planetary orbits must be like ours may well be a circular argument.