Well, I'd just like to refer you all to one episode of Extra Credits, the one about Graphics & Aesthetics. (How do I embed videos from The Escapist weekly issues on the forums?)
Take a look at Team Fortress 2 runs on Source: a comfortable, highly modifiable, open engine which isn't exactly top-of-the-line graphics-wise thus far (knowing Valve likes making nifty engine updates like the EP2 engine), but allows for beautiful settings and aesthetics, such as the aforementioned game, a prime example of "aesthetics over graphics". It's not the greatest-looking game on the market, it doesn't sport these fancy lighting effects or high-quality self-animated foliage we see in games such as Crysis, but it still looks fairly good thanks to the cartoonish setting and feel, helped by the special shaders ("lightwarps" is the technical term for the engine).
Now, about Minecraft: the game, graphics-wise, isn't the most technically-advanced in the history of gaming, either, but the "blockiness" isn't related to graphics at all: it's an aesthetics (and art, and design) choice, which accommodates for the gameplay itself (i.e. placing blocks). Minecraft does allow for higher-resolution textures and higher-poly models however, meaning you CAN make the game look better.