People generally misunderstand the role of ukemi in Aikido. Especially Aikido folks themselves. There are three aspects to ukemi:
1) as part of the "moving meditation" that contains many of the spiritual lessons of aikido; in this aspect it is non-competitive, non-violent and focuses on connection as having value in and of itself. As moving meditation ukemi is absolutely equal in importance to the Nage role since one can't exist without the other and the sophistication and complexity of each role is only as good as its counterpart. There was a reason why O-sensei tended to use only the best ukes... It was the only way he could show the best of his technique.
2) as preparation for martial application ukemi is crucial for it is in this context that students learn to connect with a partner and stay connected through complex movements. This is the most misunderstood aspect of Aikido. People who do other martial arts can see clearly that our ukemi is cooperative and they feel that the techniques are fake on some level. What they fail to understand, and Aikido folks do not do a good job of making clear, is that the cooperative method of ukemi is in preparation for effective undertsanding and application of kaeshiwaza (reversals). Every technique has certain points (I call them crossover points) at which a technique may be taken over by the opponent if you leave them the slightest opening. But in order to take advantage of those "cross-over points" you have to be connected and centered at that precise instant. If you are not absolutely locked in with your partner's movement he can make a mistake and you won't be in a position to take advantage of it. Basic Aikido ukemi is designed to prepare you for this next stage.
3) Finally, and this is also connected with martial application, there is the defensive aspect of ukemi. It goes without saying that in a fight, if you are falling, you have already made a mistake and are in deep trouble. The defensive aspect of ukemi focuses on how to avoid injury when taking falls that are designed to injure and maim. This is another aspect that gets short shrift in standard Aikido because of the way the techniques have been structured specifically not to injure. I admit that even with my own students this is a weak area as we don't practice the really dangerous and rough throwing techniques that much. If I thought my students were preparing for combat I would necessarily place more emphasis on this area but it would almost certainly result in more injuries on the mat which comes any time you push the envelope. We place a martial emphasis on our training but most of my students are professionals with families and I don't think it is necessary to take them quite as far as i might under other circumtsamces. I admit that my own skills in this area are not high as in all the years I have trained with Saotome and Ikeda Senseis I have never been thrown in a manner that was less than totally clean and clear (no matter how hard) and the ukemi was facilitated by that fact. In 23 years I have never had an injury taking ukemi from my teachers and I've taken some pretty hairy ukemi for a guy my size. So I suspect that my ability to protect myself when my partner does not have my best interests at heart could be better but I am too old to worry about that aspect of things now. that's one for when you are twenty and are still indestructible.