I think everyone else is pretty spot on. Lizardmen are, with possibly one exception, anything you want them to be. Our units do double and triple duty. Our fliers are our fast cavalry who are also our warmachine hunters. Our shooters, while short-ranged are our skirmishers (360º LOS, 2 shots and poisoned shots, yeehaw!), our chariots are also big, killer, terror-causing monsters who carry even more ranged weapons, our prime deathstar block is also a huge turtle for our major wizard who just happens to be one of the best in the game. Our rank and file infantry unit just happens to nearly be an elite infantry unit (slap in a fully-tooled hero and they get nasty!). Our "warmachines" just happen to be fear-causing monsters. The list can go on.
Because of all of this, as the others have pointed out, you can play just about any style you want. Mobile, shooty, strong magic, massive rank and file infantry, very balanced, monster-themed, horde, lots of cavalry - about the only thing we don't do is gunline.
On top of all of this Lizardmen have a lot of plastic in their line. Most of the models actually look quite nice. You can use a variety of paint schemes and they almost always turn out looking good. We have one of the cheaper armies to build as our battalion box is not stuffed with sub-par models and the models included are easily converted into heroes! Our battalion box with very easy kitbash converting can total a thousand points and if you add a Stegadon as Engine of the Gods you have nearly another 500 points.
Dark Elves are about the only other army I can think of that can compete with us in versatility but at twice the monetary investment. I don't think any other army does as much as we do with as few models as we have. Lizardmen are also fantastic for beginners, as they are a forgiving force, and also great fun for veterans as well because of all of the tactical options without being a "point and shoot" army like Demons of Chaos. Lizardmen can hang with the top tier armies as well.
All in all Lizardmen are a well-designed army on many levels. Their versatility, low cost, balance, and good looks make them a very solid choice for any Warhammer player from new to seasoned, young to old, friendly to competitive or any combination thereof. My only problem with Lizardmen is that despite the versatility, I find myself wanting a full unit of everything they have, even if I'll never play it just because it might come in useful down the line and it looks so darn pretty!