Most of the people here have really seem to have gotten off the subject, which was the question of how useful judo and aikido would be in a real fight, one's realistic chances of being able to effectively use this in combat as in full-contact, minimum-rules fighting (MMA) as you don't see a lot of these throws. I'm actually going to address this.
I happen to take MMA, including judo. (I've BARELY taken any judo at this point so I'm no expert, but my answer is based on my personal experience with it, what anyone can observe in MMA fights and what my instructor told me.) Judo has its fair share of usefulness in a real fight. However, you're right, there aren't a whole lot of throws in MMA. Hardly any in fact. I asked a guy one day why this is so and he says that throws are hard to set up. Having actually practiced some of these throws a little and have done a little pure judo sparring (I learn the different martial arts separately most of the time, so we don't mix striking and grappling), it is indeed hard. Even in pure judo matches, throws aren't something that happen very easily.
Now, yes, it's true that may be because the other guy knows what to look out for whereas if you just got in a fight with some punk on the street he may be an easier target for this. But even then, you have to be careful with throws because if you miss (fail the throw) and don't react in time to do a different technique for that (it's still possible to throw them by kneeling down instead of doing it from a stand for example) you can land yourself (no pun intended) in a lot of trouble. Think about it. You need to have the person the right distance from you, close that distance correctly, have all the parts of you and them lined up just so and must do this all in a few motions so everything works together to get the person off balance via leverage. There's even less room for error against someone bigger or who weighs a lot more. You have to often turn your back to them so if you miss that throw and they catch you (like you don't "counter" your own missed throw).... Well, I'm sure you can use your imagination.
So basically, it just takes a lot of technique and set-up to throw someone, and in full-contact, minimum-rules fighting, you also have to worry about strikes. It's easier for those guys to use sweeps and takedowns to get the person off balance and on the ground instead. (There are a lot of sweeps in judo but we're concerned with throws specifically, here.) There's less set-up and they don't take as much technique, as well as the fact that if you fail to successfully get them to the ground you're not in as much trouble.
Judo is useful in full-contact, minimum-rules fighting regardless because there's a chance you can use some sort of throw, and there's all the useful sweeps. Judo's all about keeping your balance and making them lose theirs, so that helps a lot in clinches. Oh, and there's also the various ground techniques, many of which are practiced in other martial arts, most notably Brazilian Jiu Jitsu.
So in case you're interested in learning some self-defense, I'd recommend taking up MMA with judo as being one of the disciplines included into that. I've seen my instructor spar a bit with his students and he does indeed incorporate judo into his fighting (throws kicking sweeps constantly), quite effectively I might add -- even if he is facing students who are still learning the basics of everything. You'll learn a lot about balance and balance is one of the most important aspects of any hand-to-hand fighting.
As for Aikido, yes, I have my doubts about it myself as in all the videos I've seen of it it just looks like the dudes are throwing THEMSELVES willingly as opposed to being seriously thrown while fully resisting. It looks more like a choreographed act than a simulated combat situation. And, yeah, how many MMA's do you know or have you heard of that have a background in Aikido? So far, I haven't heard of one whereas I have heard of some with judo backgrounds. However, I do like to give all things a chance and think perhaps there might be something to be gained from it, including those throws, so if I ever get the opportunity to study it some maybe I will take it.
But as for your question, I asked my instructor about the usefulness in aikido one time. He said he's studied it (not sure to what extent) and he says it can be useful in a street fight, but in MMA fighting not so much because it requires more distance and the cage/ring is only so big. You might have questions or doubts on this and I'm not too clear on it either but we didn't talk about it that much and that's all he said about it, so sorry for not giving a better answer.
Hope that helps!
P.S. The people here who are talking about being thrown or throwing so-and-so, well, I'd bet money they were all talking about pure judo/aikido sparring, and your question was regarding a real fight where you're allowed to strike your opponent, such as with a punch, as, like you said, in MMA fights you hardly see throws.
