Of course, not too many planets actually do that.
Actually, we can't do that. e>=1.0 has very specific meaning; behold:
0 < e < 1.0 ...... => elliptical orbit
e = 1.0 ......... => parabolic trajectory
1.0 < e ......... => hyperbolic trajectory
Note that for e greater than or equal to 1.0, it isn't an orbit at all, meaning the object appears once, never to return.
The difference between a parabolic and hyperbolic trajectory is this: an object in a parabolic trajectory (which can be thought of as being on the boundary between elliptical orbits and hyperbolic trajectories) will have a velocity that approaches 0 as time approaches infinity. That is to say their kinetic energy is exactly equal to the work that must be done to overcome the graviational attraction it experiences. Objects in hyperbolic trajectories have an excess of kinetic energy, and thus their velocities will NEVER reach zero, even in an infinite amount of time. In fact, their velocities will asymptotically approach some constant value, in the limit, as time tends to infinity.