Just acquired my first Arduino. Working well. Very impressed!
Is there by any chance a simple circuit which could be implemented on an Uno+Breadboard to test a transistor? Seems like a good basic functionality for the Arduino, set up a circuit with LEDs to show results. Then simply swap out the transistor for another.
What would constitute a 'test' for you? A simple result that it is exhibiting current gain? Or what's the forward gain? Or collector voltages vs base currents? A very simple test can be performed on an NPN transistor by placing your ohm meter in medium - low resistance measurement mode, negative lead to emitter, positive lead to collector, then using your finger as a bridge between the collector and base. The resistance of your finger will allow for forward bias of the transistor. The more pressure you apply your finger to the leads, the less the resistance, and the more current flow (measured as 'resistance' on your meter) will result.
It is not so simple to test a transistor unless you know the type and the pinout. I did a project that tries all the combination and gives you the answer. Unfortunately it is not a simple project but maybe you can simplify it to your own needs. If you know it is an NPN and what the pins are for collector base and emitter then it is simply a matter of measuring currents.
http://www.thebox.myzen.co.uk/Hardware/Transistor_Tester.html
Thanks to JavaBen and GrumpyMike for suggestions. I will follow up.
My immediate concern is that I have a small collection of transistors pulled from an old radio that no longer works. I'm pretty sure that the resistors and maybe the capacitors survived my learning process with the desolder vacuum pump but there is a good chance I fried the transistors. They were hard to get out. It's a wonder they were not fried going in. Sooo I just wanted to check these to see if they were operational at all.
I was able to look up the reference datasheets by putting a '2S' in front of the number printed on the transistor itself (Sony radio) and found that they are NPN and got the pin outs. However there was no flicker on the MM when I did the JavaBen test. But then I could not get a flicker from the P2N2222AG supplied in my experimenter's kit either. So not sure what is up.
The docs that came with the kit do say that sometimes the pinouts on the transistor can be reversed. This would be a helpful function of a circuit, to find out which is which.
This is where a little test circuit might come in useful. At least plugging a transistor into a breadboard is more postitive than me fumbling around with thick fingers on tiny pinouts!
Thanks.
that sometimes the pinouts on the transistor can be reversed
If you swap the collector and emitter of a transistor it still works but with much lower gain.
It is a favorite interview question of mine, and helps to distinguish book learnt people from people with real experience. 
re the JavaBen 'finger' test: you might have to select other ohm scales. If that doesn't work, if you have a good dc battery 1.5 v and a couple of resisters, you should be able to use a breadboard to test them.
Test: