Krav Maga is an excellent martial art. Although I'm no expert on its history, I believe it is an Israeli blended martial art that is taught to their police and military forces. I know a guy who used to train Krav Maga, and he was pretty good in a fight. It focuses mainly on elbows, knees, and other close up strikes. Since it's a military/police martial art, the philosophy of Krav Maga is basically that once a guy lines up across from you to fight, you need to maim/kill him as fast and effective as possible. There's not much a sporting aspect to Krav Maga.
I live near KM's National Training Center and one of my former FMA training partners directs their law enforcement program. A few months ago a friend who has an academy in Brussels flew in for some extensive training at the KM Center. I watched a number of classes. What really impressed me was that even in the intro classes, they taught some practical street techniques in every class. When students left a class, they felt that they had something they could actually use.
I was also impressed by the fact that KM did some conditioning work in each class and didn't swamp the students with too many techniques. The instructors picked a few things to work on and drilled them thoroughly.
There were also a lot of outstanding women training there, which can influence us single guys a bit.
I can't give you the best opinion because I haven't trained KM or sparred the techniques. I only observed. However, I was favorably impressed with what I saw.
I've been doing Krav Maga for a little over a year and think it's one of the better "mainstream" martial arts, although there aren't many locations where you can take it.
As stated above, it is a mixture of many different martial arts, and does include elbows, knees, and open hand strikes which I think are invaluable for self-defense. They also teach regular punches, kicks, and take-downs as well. The place where I go does not teach any ground fighting which I think is a weakness, although other teaching centers might have ground fighting.
I think Krav is an excellent foundation for self-defense because it teaches you all the basic tools and techniques. It's much more "street" orientated than most of the other martial arts out there.
I do Krav in Denver CO and have a great time. The history of Krav is pretty straightforward and you can read about it on the kravmaga.com website. Krav has changed over the last thirty years, though, and it has picked up elements of other styles of fighting. Still, it's very western in its approach. Punches and elbows are thrown the way a boxer would do them. Knees tend to look a little like Muay Thai. Some of the kicks have a Savate feel to them. The workout is supreme and we do our drills when completely exhausted, so we have them instinctively by the time it comes to a test (or a real-life attack, for that matter).
I'm not sure I agree with Colinz account of the "types" of Krav Maga, though. There is a huge difference between the things police and non-police learn in their classes, namely because police seem to be limited in the sort of force they are allowed to use on suspects. But our civilian class is about as brutal as it gets. As the levels progress, the scenarios become more "warfare"-oriented (rifle defenses and grenade scenarios), but there's nothing a soldier would do that we don't do. In fact, since the goal in a fight is to finish one's opponent, all that remains is to train the fighter to go for the kill once the enemy is incapacitated (something we don't focus on).
We do a lot of groundfighting, Raptor, the idea being that we have to know what to do when we end up there, but we certainly don't want to go there by choice (concrete is hard!). We also have a knife class that all students can attend on a drop-in basis. Note that the knife class is not associated with Krav Maga. The school has a number of different classes and the knife fighting is not billed as part of Krav. Generally, Krav Maga teaches how to use a knife in the most basic ways, but it doesn't really claim to train knife fighters.
Finally, JonesMan, I would say that there is NO sporting aspect to Krav Maga. We train to "diminsh the enemy" with every tool and skill at our disposal. There must be no possibility that he can get back up to hurt me (though sometimes that means my running away, if possible). When we do a knife disarm, we finish with a cut to the opponents knife wrist, rendering him unable to use that hand for a weapon (lest he take the knife back away from me). I would not call Krav Maga a martial art, either, but a "fighting system." It's a nitpicky distinction, but having done traditional Chinese styles for fifteen years or so, it is a real difference to me.