An anonymous poster criticized my use of LM317 chips as current regulators for high-power LEDs. While I think they are great for 350 mA single LEDs, they are clearly inappropriate for the 12 watt LED that I was playing with.
My LED was taking around 800 mA @ 12 volts. A little searching around reveals that a good alternative is the AP8803 which is a LED buck driver which can handle 1 amps @ 8-30 volts. The nice thing (aside from its 92% efficiency) is that you can set up a dimmer circuit on it using minimal parts -- or PWM control from a microcontroller.
For 350 mA LEDs, the AMC 7135 seems to be a popular choice although it's just a linear regulator, just like an LM317. Here's some AMC7135 driver hacking: http://www.candlepowerforums.com/vb/showthread.php?t=195358
and some hacking schematics: http://www.candlepowerforums.com/vb/showthread.php?t=216148
If you want ready-made LED drivers, this website has a good list of choices: http://www.videofoundry.co.nz/ianman/laboratory/research/driverlist.php
Some people are recommending the LT1618 as an option as well. It's good for powering things off USB: http://www.linear.com/pc/productDetail.jsp?navId=H0,C1,C1003,C1042,C1035,P2079
Here's a blog entry with notes: http://blog.spitzenpfeil.org/wordpress/2009/12/18/lt1618-at-work-a-versatile-boost-converter/