Here are the basics of what I've learned so far, and what I told Lauren.
Involvement is a continuum. It doesn't help to think of infrequent volunteers, team members, and leaders as separate categories of participants. These types of participants belong on a continuum. Every volunteer should be seen as a potential team member, and team members can and should be encouraged to lead.
Leadership isn't a one-way activity. You can have lots of team members acting as leaders because leadership isn't a one-way activity that only occurs when someone leads her subordinates. Participants can lead laterally when they work on projects together, and help each other overcome obstacles. They can also lead upward - people higher in an organization should be open to the contributions of those below them. Developing leaders is less about grooming someone for a position of formal authority, and is more about developing abilities like critical thinking, communication, confidence, teamwork and a willingness to take risks.
Get participants working together. You'll have real trouble developing someone as a leader if you only assign him individual work. Even when tasks can be completed individually, get participants to work together on tasks so they can learn how to lead laterally. If tasks cannot be easily split up, ask participants to choose how to distribute a bundle of tasks, and ask them to talk to check up on each other's work. This will also help you recognize which participants take the initiative, and may be ready for more responsibility. Assigning work to groups also builds morale and team spirit, and takes a load off your shoulders, as you are no longer solely responsible for assigning tasks - you can ask a team to figure out the best way to accomplish something.
Assign responsibilities, not tasks. To engage a team member's passions, assign them broad responsibilities rather than narrow tasks. People want to feel they have accomplished something, and it's difficult to feel ownership of your work if you can't see how your work connects to everything else. Almost everyone has to do some tedious groundwork; a team member will be a lot more cheerful doing that work when she decides it's necessary to accomplish the goals she's responsible for than if you tell her to do that work. Sometimes you'll have to step in to remind a team member what sort of groundwork is necessary, but even in these cases, make sure to put the groundwork in the context of her overall responsibility.
When someone first gets involved, you should probably find engaging tasks to assign them, because they may not be interested in taking on responsibilities. But as people get more involved, you should give them the chance to take on responsibilities.
Gauge a participant's interest by suggesting they invite others. People who are really interested in the work they do will probably be enthusiastic about asking others to get involved, if you have ways new people can contribute without a large time commitment. If these opportunities exist and your team member isn't interested, it may be because he doesn't feel very engaged in what he's doing. Think about how you can engage him more. If you're already doing everything you should be doing, keep in mind that he probably won't be interested in getting any more involved than he already is.
Leadership development takes time. Leadership development not only takes time in the sense of needing weeks or months; it also takes real time from a leader's day. Don't shortchange your leadership development effort by assuming it will happen as a natural byproduct of management. Keep in very good contact with anyone you're developing as a leader, and anyone who is a potential leader. Don't drop the ball!
I'd love to hear your own suggestions - how do you develop leaders?