Uses for particles

Little, since few of them are actually stable enough to live longer than, say, one second. I don't see it happening that in 10 years from now you can buy a muon emitter in the hardware store, or gluon plasma to close gaps in the walls of your house.

But what physicists do (at least, most of them), is try to explain how the world around us works. Over the last centuries our knowledge has evolved to the point where we can explain everything on large scales (mechanics, thermodynamics, electrodynamics, ...) and we are trying to discover what matter is made up of on tinier and tinier scales. This started with molecules, atoms, protons, electrons, neutrons and is currently at the level of quarks and strings. All these explanations are in the form of a theory, with which we try to do predictions and verify those experimentally. The theories we've been using so far all require those extra particles (muons, gluons, neutrinos, every particle has an anti-particle, and so on) in order to be consistent and describe experiments already done. In fact in modern physics such particles are often predicted theoretically (sometimes several decennia) before they are actually observed.
So we cannot "use" those particles in the same way we can, for example, "use" certain compound materials, for industrial purposes. But their existence shows that at least part of the theory we are setting up to explain everything we see around us must be correct. And indeed it turns out that these particles are really necessary (for example, in certain interactions that we are sure occur, they are created and annihilated in intermediate steps and the traces of those "virtual" particles are actually visible in the end result of the interaction).

So it depends on what you would call: "use". For example, many of our current technology depends on electrical conductance. Would you call this a "use" for electrons?

 

One application is positron emission tomography (PET), used for medical imaging:

http://en.wikipedia.org/wiki/Positron_emission_tomography

 

Nuclear magnetic resonance imaging, is one example

 

As others pointed out, most particle physics is fundamental research, which is not application-driven. You can also ask what uses do we have for all those galaxies we've been studying for decades now with big telescopes.
As of now, the product of that is more on the fundamental knowledge kind than it is of the practical kind. It is impossible to say what will result from that in the very long term - a few centuries ahead.

 

* Muon resonance spectroscopy
* Radioisotopes for medical treatment and medical diagnostics
* Neutron scattering to probe magnetic/spin structure of materials