Before my first units arrive, I just want to know something. What kind of army are the lizardmen? (As in are they a swarm army, a magic heavy army, etc)
they are anything you want them to be. a slann and some skink priests means magic heavy skink spam means horde saurus based means elite
skink armies are also very mobile, so if you want to control the movent phase go with them, and if you want to be somewhat cheesey you can have two eninges of the gods and have a formiddable magic power.
If you maintain the ability to move your units wherever you want throughout the game you almost always win. We have rock solid troops (saurus), meet a need skirmishers (skinks), and deadly magic users (slann, Priests on EotG) The rest of the army is filled up of really fast moving nasty units. You can do a lot of different things with it and it's a lot of fun to play.
Flexible, in that they can play many styles, but generally full of elites. Saurus Warriors are about the strongest core troop type in the game, while Temple Guard and Cold One Cavalry only serve to re-enforce the Saurus' reputation. Lots of Saurs = small, elite, hard-hitting army. Stegadons are another link in the big-and-smashy chain, too. Slann are pretty much the strongest magic-users in the game, too. Field one of those - particularly if you have a couple of skink priests to back him up - and you'll probably dominate the magic phase. One thing they're not described as is shooty, but Skink Skirmishers, Chameleon Sinks, Salamanders and Razordons are not short of ranged power, either!
As has been told; Lizardmen are a very flexible army. Most of the time however, the cheap and fast skinks will be combined with the slow(er) and expensive Saurus. Get this mix right, and your opppnent is in for a rough day. THe only thing Lizardmen don't have is long ranged firepower. Only magic can do this for us. BUt when we do get in range (whicih is not that hard!) we can fire away pretty good. My .02 The Hunted
To add to the comments on firepower... the one approach you shouldn't plan on for your lizards is a castled up sort of game. You just don't have enough long range firepower to make the enemy come to you. So by default lizardmen are placed in the "offensive" category. Build your army to get up in the face of what you think you will be facing.
I think the Lizardmen can be tailored to be either very mobile or very slow, and at the same time elite or horde. We can also go between close combat and magic real quick. As the Caneghem said, the only thing we lack is ranged fire power, but we're all about closing in anyways or having magic do most of the range work.
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 (360ยบ 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!
Our models looks spectacular as well (maybe minus our version of the cold ones...) If you like to paint you can go wild with these guys. I mean, who says our skinks have to be painted the same color? You cold go wild with bright paint schemes and these guys would still look great!