Why are the planets' orbits not completely circular?
The shape of an orbit is a conic section, in the most general terms. Under
certain conditions it can be a parabola or a hyperbola (of course you only
get one chance to view the object since these trajectories are not closed.
Closed orbits can under special conditions be circular, but far more often
are elliptical. The "reasons" have to do with Newton's universal law of
gravitation and the conservation of energy and angular momentum. Having
said that the actual derivation of the detailed equations require some
college level math (vector calculus). If it is any consolation Kepler
"knew" the orbits were elliptical by observation a long time before he was
able to demonstrate WHY that was the case. The two sites below give the
derivation for anyone who wants to follow through on the details.
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Update: June 2012