Successful clans need a lot of things, and it goes by what you determine to be successful. It varies by game, and by the nature of your organization.
To build a successful competitive clan is quite different from building a gaming organization that have members that play a variety of games.
As a former leader of a 300+ clan, I'll tell you, it sure as hell isn't easy building and maintaining a membership that is so large. It takes a lot of time, effort, and placation between your members. Some may not find it worth it, but it's definitely a different environment and a special one that can't be found anywhere else if you do it right. I think the best comparison is to consider the clan as a professional Business organization that requires a strong foundation & leadership to prosper.
1) You need to recruit and have a dedicated set of leaders. Not too large, but not too small. These should be older & more mature members of any organization. I'm not saying older = mature, but older as in having the monetary funds, expertise, as well as time to set up such an organization. It's important that these leaders get along, and that they are able to work together in an environment that requires little to no arguement.
2) Servers: You need them. A server presents the opportunity for an organization to grow and to easily recruit members. Very little clans can be launched without a public server. There's various ways to get your server population up, and I'm not going to get into that. Voice server too, as it provides a great place for members to come and just hang out. If you want to grow as a clan, you need a set plan for expanding and to continue the growth of more & more servers out there.
3) Website: A website is key to the growth of your success. It doesn't have to be fancy, I recommend a basic splash page, and a forum so your members can communicate and for the leaders to provide important updates.
4) Recruitment: Here you have to decide on what kind of players you want to recruit and if you want to have an application to a clan. From what I have seen, it's better to have two styles of recruitment, a public & a private.
In a public recruitment, simply have people apply and then a committee or set membership votes if that person is to be let in.
In a private recruitment, you give certain members the privilege to recruit people into your organization. This style of recruitment is more designed to recruit players who typically don't have a preference for a clan, or do not want to submit an application.
In addition, I like to recruit people into a probationary period, if they mess up in anyway, they can be immediately removed from your clan.
5) Ranks: You need to designate certain ranks to your players so that a chain of command & level of respect can be established. Decide on your own ranking system & such, but it is important due to the fact that it gives a sense of control & order.
This is your basic setup, from here you are given the ability to grow, to kill the clan, or to ruin it.
If you want more, tell me. Can go anywhere onto dues, weekly meetings, how to recruit...