A cold air intake is like amazing medicine that allows your engine to finally breath. Cold air intakes move the air filter towards the outside of the engine compartment so that cooler air can be sucked into the engine for combustion. Cooler air brings more oxygen (denser air) into the combustion chamber and that means more power.
However, with that said, if you install a high flow air filter where the original filter used to be, chances are you'll be causing the engine to suck in hot air from the engine which usually decreases performance, especially on turbo engines. It is advised to plan out your design to best suit your engine layout and space available under the hood. You can even consider attaching an air filter heat shield to prevent the filter from that hot air within the engine bay.
There are numerous types of air filters available such as high flow cone filters, mushroom filters, high flow box filters etc. All aim towards one function, and that is to allow more airflow into the engine. Straight out of factory, the standard air filter systems work perfectly well.
A lot of people will argue the fact that installing a high flow aftermarket air intake will drastically improve performance, however, that isn't usually the case, but it does depend on which engine you're running. Just simply getting rid of your stock intake system and replacing it with a cone filter can actually result in poorer performance due to an increase in air temperature from the engine as stated above.
If it doesn't make much difference besides a slightly more aggressive grunt, then why change it? Most enthusiasts will change their filter primarily for looks. But if you have perhaps done software and over-clocked your stock boost, your engine will require significantly more and preferably cooler air into the engine. The stock intake system simply isn't designed to handle that amount of airflow. Picture it like running a race on a hot day with a blocked nose and your mouth shut, you'll eventually pass out! Same goes for your engine.
How often do you need to replace your aftermarket high flow filter? I'm sure you're aware that for every service your stock air filter is replaced. With a good quality aftermarket filter, you can actually remove and wash them, and reinstall. After a good while though, maybe it will be necessary to replace.
So in summary, a well designed cold air intake system can most definitely aid your performance in the right circumstances, its visually appealing, relatively inexpensive, long lasting which can save money in the long run, improve the tone of the engine and turbo significantly... why on earth wouldn't you do it?