Ok, how much technical detail do you want on this? I'm going to try and be as simple as I can, and leave out all math, and as much theory as possible. If you want a detailed description of all this stuff, I'd be glad to give it. I just don't want to confuse the crap outta you...

Anyway, The bottom shield will slow down airflow significantly in the engine bay to under the car. Taking it off will allow more air to get under the car and you'll have a cooler engine. This does come at a trade off though. The airflow causes turbulence on the underside of the car, which will effect economy. If I had to put a figure on it I'd guess a 1% difference, not that noticeable, right? However, the other thing it screws with is your handling. Have you ever heard of ground effects? Well, the bottom of the car being more or less 'flat and solid' is wonderful for creating (and holding) a low pressure zone under the car, so the higher pressure above the car 'pushes' the car down on the ground. Removing the shield will let air be 'sucked' under the car, which lowers that pressure, and removes some of the down force holding you on the road. Now before you fret, its not going to be a significant amount at normal operating speeds, however when you get the car 100+ mph it can be a significant loss. The shield also blocks things from coming up and hitting the engine or any components within. Probably not a huge amount of damage if you stick to paved roads, but if you live out in the country with plenty of gravel roads it'd be best to put it back on..


OK to summarize:

Pros
- Better engine cooling
- Not have to put it back on


Cons
-Slight loss in fuel economy
-Slight loss in down force
-Have to re-attach the shield
-Higher risk of object striking components
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If you're not driving it "like its stolen," are you really driving?