Would it be entirely crazy to cover my lawn with solar panels?
I don't know about "Crazy" but there are a few issues you should consider:

Cost

This is obviously going to vary a lot depending on where you live and how big the yard is, but you're probably talking about tens or hundreds of thousands of dollars to cover a yard. 

Power Usage

What are you going to do with all that power? Many electric companies in the US allow (or are required to) let you sell back excess power to "the grid", but you usually have to have a special meter installed and often there is a limit on the size of the installation. The terms of this buy-back are unfavorable to the utility so they don't want you running a large power generator and making money at their expense.

Orientation

As has been stated by another user, the best angle for solar panels is south (if you are in the northern hemisphere; otherwise, north). The optimal tilt angle depends somewhat on the purpose of the panels but is approximately the same as your latitude. (E.g. Boston is at about 42º N so if you live in Boston the panels should be tiled at 42º.)