Powering ultra-bright LEDs like the fellow above from Sparkfun Electronics isn't as simple as powering an ordinary LED. These LEDs pass a lot of current, and can become very hot. Allowing them to overheat will damage them, and cause them to lose brightness. They need heatsinks. They also benefit greatly from a constant current source, not just a resistor. There are dedicated chips for driving these LEDs. A chip like the MAX16818 from Maxim is designed for the task, and supports dimming of the LED. This chip in particular is one I happened to stumble upon, there are quite a few others about. Maxim does tend to be very good about sending samples, so if you want to play with one don't be shy. Request a sample, glue together some boards and get going!