Picture a ball-bearing rolling through a PVC tube. The tube has holes
drilled through it, and a laser (or other light-beam) is shining
through the hole to a photodetector on the opposite side of the tube.
When the ball rolls through and interrupts the beam, the sensor on the
other side of the tube sends a signal through a microcontroller, thus
activating a 12 volt, 10 amp power supply (plugged into an AC outlet -
thinking of using a PC power supply, but if you can suggest an
inexpensive off-the-shelf alternative this would be preferable) for a
millisecond or two. I want a series of several (perhaps 6)
lights/detectors and power circuits along the length of the tube.

I have done a fair amount of computer programming and some limited
soldering/wiring, but I don't have any experience using
microcontrollers or electronics per say (in fact I'm not even sure I
need a microcontroller to do what I want). I am aware of the hazards
of using a high-amperage power supply and can take the necessary
precautions so as not to electrocute myself. If I do need a
microcontroller I'd really like one that is USB - most of them seem to
be old-school serial connections (perhaps there is an adapter?).
Thanks!

First of all: Since Your body has a resistance of usually more than 1k
depending on the body temperature (sweat) the resulting current from a
12V stabilized power supply would not exceed 12mA, which in turn is
not harmful to Your body unless applied for a longer period of time
(electrolysis).
Then: To switch larger currents most engineers will use IGBT's. These
things are rather robust, can handle large currents as well as
voltages, have a long life time and do need hardly any current to
control. IGBT stands for "Insulated Gate Bipolar Transistor" (see also
http://en.wikipedia.org/wiki/IGBT). These devices can be found in
induction generators, electric locomotives and many other
applications.

dear sir, here is how I would go about doing this... this does not
require computer, microprocessor, or programming... just discrete
components

part 1... Light sender circuit
part 2... Light reciever circuit
part 2... simple 1 stage DC amplifier
part 4... simple DC relay
part 5... your high-power DC Power supply

Part 1 circuit drives the LED's or small LIGHTS to emit and shoot the
light across the tube. This circuit could be very simple, since it is
un-intelligent, and does not do anything else. You could rig the LED's
or LIGHTS in PARALLEL or in SERIAL. If Serial, if one burns out, the
whole chain gos out.

Part 2, the light reciever circuit, uses Photo-Transistors. Each
photo-transistor is essentially a Switch that turns OFF and ON as the
ball passes.
You would probably want to put these in Parallel, so that the same
signal is generated regardless of which sensor picks up the ball. Your
circuit would need to generate a POSITIVE signal when the ball passes
the P.T.

Part 3, is a simple 1-stage DC Amplifier, built using ordinary
transistors, capacitors, and resistors. The signal coming from the
P.T.'s would feed the INPUT of the 1-Stage Amp. The Amp would amplify
the signal maybe 100X and pass
it to the output terminals.

Part 4, a DC RELAY would be connected to the Output of the 1 stage
Amp. When the AMP amplifies the phototransistor signal, the output
signal drives the DC RELAY, activates it, and CLOSES it, like a
switch.

Part 5, your power supply,  If  the Power supply were already switch
ON, then the RELAY could be used to connect the (+) Voltage of the
Power Supply to the "LOAD" at that point. You would want to choose
correct current rating on the RELAY's main lines to withstand whatever
the current is. The principle here is very simple to the HeadLight
circuit on your car.

OR... If your 10-A Power supply is plugged in, but turned OFF, you
could used the RELAY to act as a switch to turn ON the power supply
itself, replacing the manual switch in the power supply housing with
the RELAY. That, of course is more RISKY, since the poor power supply
is switching ON/OFF with every sensor activation.

summary...

LED's => shine light => PhotoTransistors => sensor signal => "Input"
of Amp => 100X DC 1-Stage Amp => "Output" of Amp =>  HI-Current DC
Relay => Relay controls the (+) Line of 10A Power Supply

An alternate sensor arrangement, instead of using Lights/LED's would
be to use  those little magnetic sensor switches that OPEN or CLOSE
when a metallic object goes by. You could mount these outside the PVC
pipe, and (perhaps) they would be sensitive enough to pick up the ball
when it passes. Their signal would then feed the amplifier.

You should be able to find Electronic Circuit CookBooks in  the local
library that explain & diagram how to set these up. They are really
pretty simple.

Good Luck!

A relay will be too slow if you want repeatable, millisecond switching
speeds at 10 amp levels.  You'll need to use IGBTs, FETs, or MOSFETs. 
If you want to make things easier, you could use solid state relays.

Making a rail gun??  If you're driving switching inductive loads at 10
amps you'll need some snubbing to cut down switching transients.

Sort of like a rail-gun, but not exactly. What is 'snubbing'? What are
'switching transients'?

Considering the comments I've received so far: I think Zodiac is right
- I don't really need a microcontroller to make this work, so that is
quite helpful as I consider how to begin. I appreciate the guidance
regarding IGBT's too; switching speed is probably important to get the
best performance out of the system.

So: other than PC power supplies, can anyone suggest a plug-in power
supply that will provide the current I need? I guess I could use a car
battery but that's a lot more amperage I believe.

Can I get IGBT's, photo-transistors, relays, etc. at RadioShack or
will I need to hunt these down online? Also, how do I know what
ratings of these to get? Thanks.