Folks this thread becomes much more readable if you go to "User CP" and tweak a few options...
To answer
espritch's question: We do collide particles together. When we do so at high enough energies, particles different to the ones we collided initially come out of the collision - and we have a precise mathematical description of how many and what types come out.
The most inutitive picture for the math (note: intuition is subjective!) is that the quantum vacuum in the region of the collision is bubbling over with virtual particles of all different types. Because theyre virtual they can't live for long, and cant trigger a "real" detector. However, by compressing enough energy in the region, you can give energy to those virtual particles, they become real and then you see them.
THe problem is that the density of the virtual particles is such that you most likely get out the low energy particles (photons, electrons, positrons, mesons etc) that we know already - so you have to do a lot of pummeling (and careful filtering) before you can spot the new ones.
Which leads to the following idea: Suppose, instead of colliding the particles in "free space" we collide them in a modified vacuum (the vacuum can be modified by the presence of nearby atoms for example). We can construct this vacuum so as to have a low density of virtual photons, electrons, positrons, mesons etc. Then less of these are produced, and the chances of spotting the new stuff is greater.
I had that idea about 5 years ago. I know that the effects of a modified vacuum can be noticed - because I found a few of these scattering experiments in which a source of "noise" was nearby atoms. However I've never gotten around to calculating something concrete (my numerical skills arent good enough). I have a close friend who is an experimental physicist on ZEUS (one fo the fermilab collider teams) and he loves the idea. However, the inertia of these huge groups is extremely large, and it would take some convincing to get them to actually do anything - which is why its on the backburner for now...
To answer
Lucy's question: Supersymmetry can appear in effective theories and not just with the fundamental particles. I vaguely remember reading about the nuclear stuff, and IIRC thats basically what they had done.
Incidentally, supersymmetry is a very useful mathematical tool - even for solving the 1D Schroedinger equation, which is the first thing we all learn. Witten showed this as an aside in a paper in the 80's - and its led to a classification of pretty much all the exactly solvable potentials.
To get some idea of this look at pages 13-17 of
http://www.arxiv.org/abs/hep-th/9405029 Its also presented simply in some textbook that I cant remember...