Question: While at lunch with my lab group we got into discussion of the different types of scattering phenomenon that we encounter in everyday life and physical experiments. We ended up listing about a dozen or so types of scattering that we see constantly, but I left unfulfilled.

I want to compile a list of scattering phenomenon and a brief description. At the very least this will be helpful for those taking the physics GRE in the near future, otherwise its a good exercise for anyone interested in physics, even those in professional physics.

I'll Begin to give you the basic jist of what I'm looking for, feel free to elaborate on the description as much as you want. An equation is useful if it's easily expressed

**Compton scattering**: Scattering of a photon off of a particle, photon imparts momentum to the particle and loses some of its energy, the change in wavelength is described by 
$$\Delta\_{\lambda} = \frac{h}{mc}(1-\cos{\theta})$$
It is independent of the frequency of the incoming photon and inversely proportional to the mass of the particle scattered from. 

**Raleigh Scattering**: Elastic Scattering of photons off of molecules and other (micro and macro) particles, photons do not lose energy but change direction. Has a strong dependence on frequency and is the reason the sky is blue (and why you can see laser pointer beams in the dark). 

P.S. I don't have the reputation to create tags yet, and there are no tags relevant to this question (big-list scattering) please feel free to retag as necessary

Answer: 
How about Newton's law $F=ma$? The force needed to accelerate 1 kg is 27 orders of magnitude ($10^{27}$) bigger then to accelerate a proton.
It's not particularly hard to accelerate anything, it just requires an energy source and time. 
The problems are merely practical:

* To go really fast you require a large vacuum. So in the case of particles we have a 27km underground tunnel (LHC) and in the case of space probes we have space itself.
* In the case of probes, there's the necessity of making them self propelled, so a lot of fuel must be accelerated too, requiring even more energy.

Given the costs, we tend to accelerate stuff as little as possible. In the case of space probe, once they reach the escape velocity of the solar system, nothing more is required.

The fastest large object is currently Voyager 1, running at $5.8\times10^{-5}c$ or 0.006% of the speed of light.