The human eye is excellent proof for intelligent design, because it is irreducibly complex. If you take out any component, it ceases to function. There is no way something like this could have evolved, because half an eye is useless. It also couldn't have just randomly happened by itself; that would be the same as a whirlwind passing through a junk yard and forming a Boeing 747. Therefore it must have been designed by some sort of intelligent creator.
It's the principle that the eye is like a basic arch bridge, where removing any single stone causes collapse and you no longer have a bridge. The thing about the Boeing 747 is completely extra, but I've included it because it was in the initial source of irreducible complexity and as a result also seems to be included with every single repetition of the concept by mindless individuals. I bet any time I link to this entry as a response to this argument, the 747 idea will have been included maybe nine out of every ten times.
One of my first arguments against the idea that God created our eyes is more a theological one, which is to say that our eyes actually suck compared to a fair bit of the animal kingdom. We can see in colour, but our movement and peripheral vision aren't nearly as good as some animals. You've also got creatures like the Mantis Shrimp, whose eyes completely obliterate ours. Their eyes can see polarised light, and there are successors to Blu-Ray that are looking to copy ideas from the Mantis Shrimp, so to say God gave us the gift of sight is a bit of a double-edged statement, because he sure could have given us a far better gift.
Anyway, on to the proper point.
The eye is undoubtedly an incredibly complex organ. Anyone who had studied Biology to a reasonable level would probably agree when I say that actually, pretty much any organ you could care to name in the human body is incredibly complex when viewed in detail, and amazing in it's own way at doing what it does, but the eye is the one that's usually used in the argument of irreducible complexity (if not, wings or brains are).
It is indeed true to say that half an eye is going to be useless, but only if you cut it in half with a knife, which isn't ever going to happen in nature through genetics. However, I'm pretty sure if you remove any single component of the eye short of the optic nerve, it's going to be far from useless. Sure, it won't nearly be as good as the finished article, but we're talking about early evolutionary principles here. Remove my lens and sure, I'll struggle to read stuff and see at a distance, but I'll still be able to detect movement and things. In a struggle for life against something which was entirely blind, I'd be far better equipped to catch prey or escape predators. The argument of irreducible complexity is based on the idea that there's absolutely nothing in between a human eye, and a completely functionless one.
For example, if we go back in time to the point where no animals had eyes, before the eye had appeared through evolution. If one animal genetically mutates in such a way as to form what's basically just the optic nerve, the most basic form of eye, a single pixel, black or white. Compared to what we have, it's useless, it's almost inconceivable how it would benefit, but compared to being completely blind, would it not offer a benefit?
You can take quite a gradual set of intermediate stages between no eyes whatsoever and human eyes. There are plenty of traits you can slowly level up and increase together to get to the finished article, and it'll fit perfectly into evolutionary theory as well. Animals that have eyes with better movement recognition will be able to escape better from predators than animals who don't. Better resolution (ie. the fovea), the ability to focus, wider peripheral vision, the ability to see in colour, all of these providing various advantages in the wild, increasing the chances that the animal will survive and pass on it's genes.
If anything, the eye is the worst example of irreducible complexity for fans of intelligent design to pick, because unlike other organs such as the liver, it's extremely easy to see how any minor improvement would directly increase the mutated animal's prospects of survival and passing on their genes.
The other example used aside from the eye, though not usually used by the sort of dumbass creationists you tend to find dispersed throughout the internet, is that for the bacterial flagellum, which is the little spinning tail thing that bacteria use to move around through fluids:
The flagellum is quite an intricate and clever system of propulsion, given that it operates on such a tiny molecular scale. I'm not an expert in microbiology, so I can't really explain in this how something like that operates, let alone how it could possibly have evolved, but luckily and importantly there are people out there who can: http://www.talkdesign.org/faqs/flagellum.html
That's a pretty heavy and long scientific document, and I don't remotely expect anyone to read it all, but the summarising first paragraph is all that really matters. It's possible to see how it could have evolved in stages, and that beats the irreducible complexity argument.
Really the irreducible complexity argument is instantly destroyed if you can find a way from nothing to the finished article in fairly logical and plausible small steps, where each individual step preferably offers a benefit over it's predecessors, or at the very least doesn't add a disadvantage. If you know enough about the subject, then it's usually not that hard to do this, it's just that fans of intelligent design tend not to think of it that way.
Anyone interested in further reading on irreducible complexity, creationist examples and proofs as to how they're not irreducibly complex should try here: http://www.talkorigins.org/faqs/behe.html
I'd also like to say, as a footnote, that the Boeing 747 can't really consider to be intelligently designed either. It wasn't formed by a whirlwind going through a junkyard, but it was the result of years of hard work, a lot of trial and error and a lot of borrowing from previous ideas. It came about as a result of human thinking and ingenuity, rather than principles of nature and natural selection, but it's not that tenuous to suggest that it was an evolutionary-style process that actually formed it. Mankind just reduced the timespan to a couple of centuries (or millennia if you want to be picky) instead of the couple of billion years that it took nature.