Trevor Powell has a very good answer.
Also if you consider that Unity3D, while big enough to be known, is not used by major company's. Bigger Company's like Blizzard, EA, Bethesda, and Square Enix, will build their own engine, or purchase the rights to use something like the Unreal engine. And then will put lot's, and lot's, of time into making the game large, unique, and in general try to come up with something original. Something that's never been done before.
On the other hand people starting up, or working for free, aren't worried or spending 2 year's of full-time work with a team of 100 people, to make an original idea come to life as the next big internet sensation. For example you can find THOUSANDS of different games of tetris, created by people trying to learn to program. And they all look the same! Regardless of if they where programmed in Basic, C++, DirectX, or OpenGL, it's tetris. However, There aren't many people trying to remake Skyrim.
Unity3D fall's kinda in the middle-ground between those two end's of the industry. It's got people who are aiming for something more complicated than tetris, and people who are copying idea's, and mechanics, from a variety of very well known (modern) games/genres. So you wind up seeing something fairly familiar but still somewhat impressive, though not spectacular. And people making that form of game happen to typically use Unity for it's familiarity, power, and lack of expense.
In effect, your not recognizing games made with Unity. Your recognizing some basic trait's of the developers, who tend to use Unity.