Well, this is a great question, and I must say beforehand that my experience with an organization of villains is pretty narrow. But I do hope that what I'll write here might be of some use to you.
One of the key things that you can do is to find inspiration for your villains in other sources. I once based an organization of villains around the 7 exes from Scott Pilgrim vs the World. Another time it was around a bunch of villains from westerns. The trick is to find some villains that are cool and draw inspiration from them.
This inspiration can be in terms of copying the villains, or it can be in terms of taking certain parts of their personalities. It can even mean analyzing what made them so memorable and using that someway.
Make them somewhat related to the characters
You want your players to care for them, to remember them, or something around those lines. For that, you have to make them related somehow to the PCs. While having them compete for the same goal is nice, I do prefer something closer to the trick utilized in Scott Pilgrim, having them the exes of a certain friend, relative or the like. Maybe have some of them be immediate family of the PCs? A true connection is far better in order to make the players care for them enough to hate them, love them, or even love to hate them.
Make each one of them unique
This is also very important. While they are all a part of an evil organization, they must be unique by themselves. Each and every one of them is also a villain that the party will have to encounter one day or the other. In Hot Fuzz each one of the conspiracy members is unique and is colorful enough to be remembered. We have the couple who hate the reporter for stating the wife's age is higher than it really is. We have the farmer whose mother has a rifle. We have the chief of police who doesn't punish criminals and we have the manager of the Supermarket who is always there when you least expect him. In Scott Pilgrim we have the Female ex who Ramone experimented with, we have the actor who has doubles, we have the leader who is an agent and who can control Ramona and so many more.
Go for it too, make them unique, make them colorful, make them come alive as persons and not only is a part of an organization. The fact The Joker fights sometimes alongside with Bane doesn't make each one of 'em less frightening, unique or evil, right? Why should that be the case here?
Have something common for all of them
Being unique doesn't mean that they have to be completely different. In Scott each of the exes is an ex of Ramona, and an idiot. In Angel they are all attorneys. In the first and second seasons of Buffy they're all vamps. Have something that unites the villains that is common to all of them. Maybe all of them have similar clothes or use the same perfume? Maybe they all talk a bit funny?
As a bonus, if you can make the uniting thing a thing that is cool and all by itself, which can make alone the villain stand out, it is even better.
Let the players know of them in advance
The characters should know about the organization pretty early, but having the players know about the organization even earlier can do magic sometimes to your campaign. If they'll know that their characters will fight an organization of villains, the players will look for them (and with far greater anticipation). Always remember that the players are authors as well as audience, and if they will be looking forward to meeting the villains they will far better enjoy this meeting between their characters and villains. But they will also search for them; lead their characters to them, and so much more.
I also highly recommend reading answers to questions like these two. While they do center on creating a single villain, they are still quite useful and in more than just creating and fleshing each and every one of the villains in the organization.