You bet! Particle physicists make this kind of reaction happen every day in laboratories. This accomplished by accelerating ordinary particles up to very high speeds, close to the speed of light, and smashing them into each other. In an interesting collision, the result is a spray of new particles, many of which may be heavier than the original pair that collided. The energy of motion of the original particles has contributed to creating new ones. Some of these new particles are very interesting and exotic! Most only live for a short time before decaying into more ordinary stuff.
It is in this way that scientists have found out what kinds of particles exist. The world is made up of stable particles, and we only know about the unstable ones because we have been able to create them in the laboratory out of the energy in the collisions.
There are rules of course. Whenever a particle is made, certain things have to add up. The energy has to add up, of course. The total electrical charge cannot change, and so when many kinds of particles are made, the same number of antiparticles must also be made (some particles are their own antiparticles so you can make one of these at a time. Photons are examples of this). Antimatter annihilates with corresponding matter particles, and the result is eventually photons, leaving no net new matter.
Scientists are currently studying the differences between matter and antimatter in an attempt to explain why the world contains so much of one and none of the other.
You can find out more about particle physics experiments by visiting the web sites some laboratories:
You can also find out all about the particles that have been discovered at these and other laboratories at The Particle Data Group
at the Lawrence Berkeley Laboratory in California. I recommend looking through the "particle adventure" link first to get an introduction to the field.
(published on 10/22/2007)