[DoronS]

Our team has over 100 members on our official roster, and we've developed some strategies for dealing with that.
In terms of recruitment, we'll accept anyone who wants to join our team, and have no application process. All that we require is that team members maintain their grades (>=85) and fulfill a volunteering requirement. We probably get around 75ish newbies every year, but by the end of build season, most of them leave, and we're left with around 25. Out of these, perhaps 10 will eventually be fairly dedicated to the team, and 5 will become "core" members. So, out of 100ish total members, only half are fairly dedicated, and only about twenty are considered "core," and end up getting leadership positions.
To handle our numbers, we've divided ourselves into one FRC team and two FTC teams. Each team competes separately at the NYC regional, but during the build season, we hold concurrent lab meetings. If I was to make a guesstimate, I would say that we have about 20 FTC members, but there are always some FTC people who work on FRC projects and vise versa.
Within our FRC team, we are divided into engineering, programming, and marketing. People can switch divisions whenever they want, and this often happens before people settle on one area. In each area, if there are a lot of people, we'll try and delegate our projects as much as possible in order to expose members as much as possible to the team. For instance, in engineering, we'll have one core member be director of field construction. That person splits up a group of team members into specific projects, such as building a trailer or peg wall, and is responsible for making sure everything gets done in the end (by teaching everyone how to do everything), but everyone does the work.
I'd like to point out that we do have the advantage of having a fairly large working space in a school of 3,300 students, but I believe many of the division and delegation strategies can be used to run a team efficiently while still affecting the maximum number of people possible.