What is the most oblate astronomical object known? There are some very vast spinning objects out there.   How high can the eccentricity get, or, which I think is easier to understand, how small can the ratio between the polar and equatorial diameter be?

For clarification, I'm asking about objects composed composed of particles (not some boundary or field etc) and that are devoid of non-microscopic empty spaces. I.e. a planet or star etc; not a galaxy or rings or a heliosphere etc. 
For the purpose of this question, I just don't find galaxies or nebulae interesting because they can have almost any shape.

I'm talking about structures that are oblate spheroids essentially.
Saturn is the most oblate planet in the solar system. If the equatorial diameter is $a$ and the polar diameter is $b$ then its oblateness, $(a-b)/a = 0.1$.
We do not know the oblateness values for more than one or two exoplanets and even these are somewhat uncertain, but are thought to be lower than Saturn's value. For example http://adsabs.harvard.edu/abs/2010ApJ...709.1219C
The oblateness of a star depends on the ratio of it gravitational acceleration to centrifugal acceleration at the equator. So the most oblate stars ought to be the ones with big radii and fast rotation rates (i.e. types of stars that would have low surface gravities if non-rotating).
Giant stars come in two basic types - red giants, which are evolved intermediate and low-mass stars. These tend to be slowly rotating, though there is a class called FK Com variables which are fast-rotating red giants.
The other class is the blue giants, which are high mass main sequence, or slightly evolved, stars.
For maximum oblateness you want the star with the highest value of:
$$ f = \frac{R \omega^2}{GM/R^2} = \frac{R^3 \omega^2}{GM}$$
where $M$ is the stellar mass and $\omega$ its angular velocity. Often we don;t know $\omega$, but can estimate the rotation velocity at the equator $v=R\omega$. Hence
$$f = \frac{R^3 v^2}{GMR^2} = \frac{Rv^2}{GM}$$
A possible record holder is the O-type star VTFS 102 in the Large Magellanic Cloud.
This probably has a mass of $25M_{\odot}$ a radius of about $10R_{\odot}$ and has a measured rotation speed of $\geq 600$ km/s. Thus its value of $f$ is 0.75, compared with a value of $f=0.15$ for Saturn.
EDIT: Due to Michael B - what about &quot;millisecond&quot; pulsars? The shortest periods are about 1.4 ms, the radii are about 10 km and the masses are likely to be about 1.4$M_{\odot}$. Do the sums and you find $f=0.1$. So, (at least in Newtonian mechanics) they should be no more oblate than Saturn.
A further contender might by the dwarf planet Haumea that orbits at 40-50 au from the Sun. It is thought large enough to have achieved its shape via hydrostatic equilibrium between gravity and internal pressures (and rotation). Its mass is $4\times10^{21}$ kg, (mean) radius is 700 km and it has a rotation period of 3.91 hours. These numbers give $f=0.25$. It has been modelled using this, and matching its light curve, to be a triaxial ellipsoid (rather than oblate) with axis ratios 2 : 1.5 : 1 (http://adsabs.harvard.edu/abs/2006ApJ...639.1238R).