We can put a full information "kit" here about how to start a school computer club centered around programming, including suggested organization and activities. We can maintain a list of links to sites for clubs that people have started, and coordinate "contests" and other events involving them all.
Fill in your ideas and elaborate on other peoples', and we should have a plan in no time. 
Particular clubs
Gosh. No one has come along with ideas. I know there were some people who shared plans about starting school computer clubs. Would you please step forward and add blurbs about your plans here? -- AdamChlipala
General ideas
Since there is a request for information, I guess I will go ahead and post my ideas here. Last year at my school, I helped start a computer club. There was already a robotics club at the school but no one (except for the two or three kids that started it) showed any real interest in it. The teacher in charge of the group, Mrs. Smith, told us that and we decided, in an attempt to revive the club, we would expand the group's interest range to something very general. We chose "technology club." We alerted the office of our "new" club and they made announcements. This brought a few new people in, and we ended the year with a total of about 8 members. The point here is that if "programming club" or other specific names do not bring in members, change the name to something more general and introduce them to your personal interests at a later time. Chances are, if they'll join the club, they'll be open to new ideas and activities and will trust you as a mentor. If this occurs, you can show them HProg as a way to learn outside of school. -- MikeNolan
If your school ever participates in programming contests then advertising that (using the prizes offered by the competition can be a good idea - I recall "Win a new computer" being advertised at my school) can bring in interested people. Often you have an excuse to pick and choose who you take in the club too (under the guise of selecting the best for the competition).