Why does a rubber band become a lighter color when stretched? I was stretching a pink colored rubber band, and I noticed that the longer I stretch it, the lighter the pink becomes. I haven't found answers to this question anywhere else. Is there a reason for this phenomenon? 
Why does this happen?
 A: Colour can come from pigment particles embedded in the translucent rubber matrix absorbing light. When you pull the band the particles become separated by a longer distance, but being themselves inelastic remain the same size. Hence the amount of absorption per unit area decreases, and the band become lighter in color. 

Simulated rubber band with pigment particles embedded in the matrix. As it is extended it becomes more translucent
Rubber bands are also incompressible ($\nu=1/2$) so the volume is largely unchanged by pulling. This has the effect of reducing the cross section, further reducing absorption.
A: Rubber bands are made of polymers (more specifically elastomers). A given polymer in the band can either be aligned with other polymers around it, or it can be misaligned. Therefore, you can end up with regions of order and regions of disorder in the band. In an unstretched band you have much more disorder, but when you stretch the rubber band you are forcing the polymers to become more ordered and aligned$^*$. It is this alignment that changes the optical properties of the band, causing it to scatter light differently and appear to be more white.
Relating this to Anders Sandberg's answer, unstressed the rubber is more transparent, but stretched the rubber is more opaque, thus causing fewer pigments to be visible.

$^*$This also explains why heating up a rubber band causes it to shrink, as the extra energy causes the polymers to become less aligned, which causes the band to decrease in length.
A: Stretching rubber makes it shiny

Image credits: onelittleproject.com
We know, balloons become highly reflective after inflation. This effect applies to rubber bands too. Rubber has a highly coiled structure, which scatters light randomly, giving it a soft appearance.

Image credits:Balloon science
Upon stretching, the coils unwind and reflect more uniformly, which gives it a shiny look. This answer and this answer elaborates this effect well.
So, on stretching a rubber band, it becomes more reflective, which means more light would reach your eyes, giving a perception of a lighter colour.
Presence of surface impurities
It may not be relevant, but the presence of surface impurities affects the colour change. In real life, rubber bands tend to gather dust and other contaminants over time. For ancient rubber bands (like the one I have) there is a complete layer of dark coloured impurities coated on its surface. 

Here are some close-ups. You can see that the surface impurities are more spread apart in the stretched band.

Stretching the rubber band exposes the colour of  'fresh' rubber inside.
This answer offers a good explanation.

Here, I would like to emphasise the reason why I haven't considered the transparency effects.
Transparency does not always imply 'lightness'
A stretched rubber band is indeed more transparent than an unstretched one. But does that make the rubber band lighter? 
It does, only when you view it against a brighter background. 


As you can see, even in the dark background, the stretched rubber band is still lighter than the unstretched one. This shows that for my rubber band, the reflectivity effects are predominant over the transparency effects. This may not always be true and depends on various factors like the thickness of the band, type of rubber and pigment density.
Transparency effects are much more noticeable in thinner objects, like rubber sheets. Interestingly, this effect can be exploited for making smart windows, that can precisely control the amount of light passing through it.

Credits: MIT

A: In general the rubber from elastic bands scatters light. This explains why rubbers are opaque, but still reflect light quite a lot, in the same way as milk looks white.
In the presence of pigments, the whitening when pulled can be explained if the material scatters light more when it is stretched. More scattering means that light rays that get reflected, or scattered, at the surface of the rubber have to travel a smaller distance through the material before getting reflected. Hence, they have less chance to hit a color pigment. (Pigment density remains constant, as rubbers are fairly incompressible.)
The remaining question is: Why is scattering larger when stretched?
From this source:

From these, it is concluded that:
(a) Optical heterogeneities are present in stretched samples having a size of the order of several microns.
(b) These heterogeneities are not present in the unstretched samples and develop with elongation in the same (or lower) elongation range where crystallization occurs.
[...]
(d) The heterogeneities primarily represent fluctuations in the orientation of anisotropic bodies rather than fluctuations in density. [...]

Aaron was on the right track by mentioning scattering, but it seems that heterogeneities in the material are more relevant than crystallization to explain the whitening by light scattering.
A: Anders Sandberg explained the main effect (in fact, decreased per-area pigment concentration and the band becoming thin are the same effect).
There are two more effects that acts even for non-translucent rubbers, making them whiter:


*

*The presence of tiny cracks on the surface. When stretched, they open wider. One can see the same effect on macro scale in aged rubber. The cracks allow more light to scatter instead of going deep in the volume of the material and being absorbed (the same effect makes the snow white and the deep water black, blue or whatever less white).

*The presence of tiny voids in the bulk of the rubber, containing filler, pigment, air or just a discontinuity in the polymer. When subject to negative pressure, these also expand and scatter the light more than in non-stretched state.
A: It is very important to understand that contrary to popular belief, Sunlight is white light (not yellow). 
Now you are asking why does a rubber band become lighter colored when stretched, and your question can be why does a rubber band refract/reflect more light when stretched without changing too much the (distribution of) energy levels of the photons, more specifically why does the refraction/reflection contain all wavelengths of photons (thus combining into more and more whiter/brighter light).
Now the answer is crystal lattice structure. There are certain materials that have this kind of molecular structure, like glass, crystals, and certain plastics, and they have the ability to refract and reflect light (visible light too) without changing too much the (distribution of) energy levels of refracted photons and more specifically able to refract/reflect all wavelength (visible too) photons and absorbing very little.

http://www.schoolphysics.co.uk/age14-16/Matter/text/Rubber_band/index.html
Now what happens to rubber bands as it gets stretched is that the molecular structure of the rubber is able to change, and it changes towards these crystal lattice structures of certain materials (glass, crystals and certain plastics), and thus is becomes able to refract/reflect more light without changing too much the (distribution of) energy levels of the photons, more specifically, it becomes able to refract/reflect all wavelength (visible too) photons (thus able to seem colored more like the light in the environment).
It is a very good example, if you try to stretch a rubber band in a room filled with dark blue light. When you stretch the rubber band, it starts to refract/reflect more dark blue light, and in fact you could see the rubber band seem to becoming darker (not brighter).
Another very good example is the balloon, try to fill the balloon with air and see as it seems to become lighter in color, but do it in a dark blue light filled room, and the balloon might seem to become darker as you fill it with air.
