By the question I mean that the planets spin in their ellipse but all ellipses describe the surface of a near-sphere shape around a star.
Same question but for a solar system with 2 stars of irrelevant sizes or nature
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I think what you mean is - is it possible for a planetary system to exist such that the planets do not orbit in a single plane, but the planets have a large scatter of inclination angles?
Our solar system has a relatively modest range, providing you ignore Pluto, of orbital inclination values (and eccentricities); zero to 7 degrees (Mercury). This is thought to be due to the way that the solar system was formed; from a rotating protoplanetary disk.
Other planetary systems are thought to form in the same way and indeed there is evidence from many of the multiple planetary systems discovered via the transiting technique, that many other planetary systems are also very "flat" and often flatter than our solar system. (e.g. Fang & Margot 2012)
Nevertheless there are exceptions. One can use the Rossiter-Mclaughlin effect to estimate the projected orientation of a transiting planet's orbit to the equatorial plane of rotation of its parent star. There are many examples of planets which have orbits that go over the rotation poles of their parent stars or are even retrograde. For example: Anderson et al. 2010; Triaud's 2011 PhD thesis. About 1/3 of "hot Jupiters" are misaligned in this way.
The misalignment may be as a result of dynamical interaction with other planets or as a result of close fly-bys by other stars or interactions with a binary companion.
EDIT: The R-M effect is suggestive of non-coplanarity, but as only one planet is seen, it is not conclusive. There is at present I think only one solid example where the measurements suggest non-coplanarity of two planets and that is in the planetary system surrounding Upsilon And A. Using radial velocities and astrometry from the fine guidance sensors on HST, MacArthur et al. (2010) were able to establish that the c and d planets (i.e. the 2nd and 3rd planets in the system) were inclined at angles of $30\pm1$ degrees with respect to each other. This is much larger than the differences seen in our solar system (maybe 7 degrees).
The presence of two stars is something that is thought to be a key trigger of misalignment. Something called the Kozai mechanism can cause a periodic exchange between orbital inclination and eccentricity so that a planet flips backwards and forwards between two radically different orbits. It is quite possible for an outer planet to be affected by Kozai cycles whilst closer in, perhaps more massive planets contine on their more "usual" co-planar paths.
If you would like (much) more information then a good read is the review by Melvynn Davies et al. given at last year's "Protostars and Planets VI" conference. The talk can also be viewed here (he's a good speaker).