@Eriba: thanks, I hadn't heard of that yet; it seems very useful.
@Mark and Nick: Thanks for your insightful replies. I understand what you're saying, but then I don't really get how a 7-segment LED could work. I have one that has a common anode to which you attach one resistor, and current can then flow to between one and seven different led's (datasheet: http://www.sparkfun.com/datasheets/Components/YSD-160AR4B-8.pdf). So how can the led's in this display work in parallel with just one resistor? According to the datasheet there don't seem to be any internal resistors?