Just thought I would put in my two cents here. For some context, I have been studying Danzan Ryu Jujitsu for about 20 years now. For the last 4-5 I have been training Kenkojuku style Shotokan Karate as well. The dojo I rent space out of, primarily teaches Aikiko, but they have a lot of other Japanese arts their as well, including Daito Ryu Aiki Jujitsu. I get the opportunity to get on the mat and train with the Aikido guys quite a bit... and unfortunately to a lesser extent with the Daito Ryu guys as well.
My take on Aikido is similar to what many have mentioned here. It is a finishing art, as in you already know some other arts before starting Aikido. As you move through the Aikido patterns, they are quite lengthy, but do offer many opportunities to apply other arts to short circuit the Aikido pattern. However, as the student, you need to recognize where these places are. The pattern will open targets to punch or kick and provide places to enter for a number of different throws. The more you bring to the table, the more opportunities you find. However, many students start with Aikido as their first art... and thus don't understand what they are missing. When they go on to be instructors, there is a lot to the patterns that they don't understand, in my opinion.
The patterns for Aikido, are sometimes long and intricate. They seem to require a partner who knows the other side of the pattern and who needs to be willing. To me, this is like learning ballroom dance. At first, both the lead and follow need to know where to go. In order to become a good lead, you need to work with patient follows, who know where they need to be and who can give you feedback on how to lead better. With dance, you get to a point where you can start to lead a good follow, without the follow knowing before hand what is coming up. Eventually, you can lead even a beginner, with no knowledge what so ever, into at least the basic moves and more as you get better as a lead. However, at the beginning you need the cooperation.
I feel that a lot of time, people think Aikido is about the end of the technique... where the guy falls down or taps out. In my opinion, this is due to the lack of other martial arts experience of the student. By the time Aikido gets to the "make him fall down" part, you have already passed many opportunities to punch, kick, lock, take down or throw the guy. You didn't, because you were following the pattern. Aikido is about the very first part of the technique. Can you immediately off balance and compromise your opponent and can you keep it? If you can, you can use it to set up any number of much more effective techniques to end the confrontation.
So why the long pattern? I look at it like adding a really long lever to a small precise movement. By adding a really long lever, you can work on making the movement slowly, applying the right pressure at the right time, in the right direction. As you get better, the lever can be shortened. Eventually, no lever is needed.
The question is: Is it effective? In all the rolling / sparring I have never been able to apply an "Aikido" technique to my opponent. I have however, been able to better employ certain principles. It has helped me develop a better feel in some cases, helped me break their balance and or structure easier in other cases and even develop more leverage. However, remember I said I was a DZR guy? Well, the Shotokan has also given me improvements in all those same areas. So has the bits of BJJ I have worked on, as well as the Daito Ryu... All of them, have helped me improve my DZR. All of them have shown me things my Sensei has been pointing out to me for years. Here is the thing though, each one of these arts has given me different insights and different improvements to the same techniques and to the same principles.
So, is Aikido the best way to learn these extra finishing bits? Is it the fastest way? I don't know. I know its not the only way. I know it has shown me things that other arts have not, though that may be due the denseness of the student, in my case. Comparing it with Daito Ryu, I find Daito Ryu to do the same thing, only more directly... in an opposite kind of way. (one enters when the other yields and vice versa) I find Daito Ryu to be a bit more complete for a combat art.
In the end, I find Aikido does bring some things to the table, if you look at it right. Its about that initial contact... not the finishing of your opponent. The long complicated patterns, are levers to make certain motions much bigger for the student to see and feel. That pattern also provides many opportunities to short circuit and finish the opponent, but these are left for the student to find and fill (or bring with them). Just like in dancing, those long patterns, with a cooperating partner, will allow you to develop a feel for what the other guy is doing... you will feel him resist, much sooner. Some of the patterns have that resistance bit built into them, slowed down and magnified, so that you can practice dealing with it.
In the end, I think everyone has to evaluate how they spend their allotted training time. Aikido has a lot of things to offer, but its not for everyone. It also helps if you know what it is giving you and what it is not. But that is true for all arts.
Anyway, these are just my opinions based on the experiences I have had. Would I recommend it for a guy getting ready for an MMA match or going out to be a LEO? No. Would I recommend it to an experience martial artist looking to fine tune some things, or who might be looking to get off their current plateau? In this case, it would be worth trying out. If you just enjoy it for the sake of enjoying it or want exercise or to work on range of motion... sure go for it.