The word "amateur" is highly contentious among astronomers. Technically it means someone who is not paid for the work they do, but it has connotations of meaning "not well done" and "poorly thought-out".
When it comes to astronomy, that's just plain silly. Amateurs may not get paid to do astronomy, but in many cases they are every bit the equal of professional astronomers. And sometimes they eke out a lead, too.
Such is the case of Arto Oksanen, a Finnish amateur. On October 10 of 2007, using a 40 centimeter (14") telescope, he found the optical afterglow for a gamma-ray burst, a titanically powerful explosion created when a massive star explodes and forms a black hole. GRBs produce light across the electromagnetic spectrum, but they fade to invisibility incredibly quickly, usually within minutes or even seconds. This makes observing the afterglow very tricky.
Recent advances have made it easier: telescopes in space (like Swift) detect the GRBs and send down the coordinates of the burst within literally seconds of the discovery. If you have an automated telescope, and subscribe to the email alerts, you can chase down the afterglows. But you have to be fast!
Oksanen was fast. He found the fading optical blast from GRB 071010B, the second GRB detected on October 10, 2007 (hence the GRB designation) just 17 minutes after the burst began, when it was at an optical magnitude of 17.5 (about 1/40,000th as bright as the faintest star you can see with the unaided eye). This quick work beat out the professional astronomy community, and provided critical observations of the early time activity of the burst, which provides key insight into the physics of the explosion.
Follow-up observation of the burst by the massive Gemini and Keck telescopes indicated it was at a distance of 7 billion light years away. That's a pretty fair distance to be seen by a 14" 'scope. While I'm sure Oksanen's setup is pretty sophisticated, in fact that kind of telescope is not too expensive as things go. And hey, isn't gift-giving season coming up...?