[Ecky]

Many air intakes are "tuned" to smooth out power delivery across the RPM band. So, by removing it, you may be losing torque in one place and gaining it in another, usually resulting in more "lumpy" power delivery. This may or may not matter to you; it certainly doesn't to me. In fact, I have my stock snorkel removed and replaced with dryer ducting to suck warm air from around the catalytic converter.

The good: Warm air intakes almost always improve economy, up to a point. I don't think my car starts to retard timing until the intake air gets around 180F, and I've aimed to have the incoming air be around 115-125F. In the winter this can be a 10-25mpg improvement where I live, when the air outside is 40 below zero.

Warm air improves economy directly by reducing power - warm air is less dense, resulting in the throttle plate being more open and thus lower pumping losses. Cold air lowers economy in gasoline engines, but improves power because you can get more air into the engine. If you want the best of both worlds, you want a flap or valve to feed your engine warm air at part load, and switch over to cold under heavy loads. One car that had this, to my memory, was the Honda CRX. The power gained under load and the economy gained at other times was far larger than the reductions caused by the weight of the system; removing it would be akin to unbolting a turbo from a TDI to save weight.

The bad: Almost all aftermarket filters allow more dirt into your engine than the factory air box, and rarely improve anything for a stock engine.