Why is the solar system flat but the planets spheres?

[teleskopjo]

why didn't the planets flatten out as well whilst forming ? (conservation of angular momentum etc. as it applies to the solar system formation).

[michael.h.f.wilkinson]

It is a matter of a balance of forces. When the density gets high enough, gravity overcomes the centrifugal effect of rotation. The average density of the solar system is many orders of magnitude lower than that of even the least dense planet (Saturn), so the gravitational forces are weak hence the flat structure. Note that planets are slightly flattened (Earth included), especially rapidly rotating bodies like Jupiter and Saturn.

[ollypenrice]

I'd never thought about that but now I have! Thanks for both the question and the answer.

Olly

[Knight of Clear Skies]

The dwarf planet Haumea is thought to be this shape, due to its rapid rotation and low gravity:

There are also non-spherical stars such as Archerner:

As to why the solar system is a disc that's a tricky one that I struggled to visualize for a long time. it formed from a collapsing gas cloud full of chaotic motion, but on average it was spinning slightly in a particular direction. As the cloud collapsed this net angular spin was exaggerated due to collisions between particles and gravity, causing it to flatten out into a disc.

This Minute Physics video explains it a lot better than I can:

[Ronnie67]

Conservation of angular momentum if what causes clouds to flatten out into a disk. The interstellar dust and gas cloud that the Sun and Solar System formed from, along with other stars. started to rotate when the bow-shock wave of matter and energy from one or more relatively nearby supernovae encountered the interstellar dust and gas cloud. The other stars that formed at the same time that the Sun did dispersed long ago. If you want to look at a relatively young open star cluster that still has traces of nebulosity around it, look at the Pleiades with binoculars after sunset tonight. 
If you have REALLY good naked eye vision, you might even be able to see the tiny Little Dipper shape of the brightest of the Pleiades. There's another open cluster called the Hyades relatively close by that bright orange giant star Aldebaran is in front of. Aldebaran is the "eye" of the bull constellation of Taurus 

Clouds interstellar gas and dust clouds flatten out because of conservation of momentum mass and energy. This does NOT completely explain some planetary systems. When astronomers started discovering planetary systems with planets that revolve around their primary star in the opposite direction to the star's rotation, scientists originally said "That can't happen, because it violates the conservation of mass/matter, energy, and momentum". Some OTHER forces acted on planets with orbits like that AFTER the planets were formed. Scientists gave a name to the effect using the last names of two people that begin with "M" and "R." 

[michael.h.f.wilkinson]

The Pleiades are certainly young (presence of OB stars gives that away), but the nebulosity surrounding them is not a remnant of the clouds out of which these stars formed (as was initially thought), but just dust these stars are moving through.