Why care if there is water in your compressed air?

The process of compressing air generates free water, and increases air borne water vapour. If you are not sure about why this occurs, take a look at the article on this site entitled "Why does water run out my compressed air line?".
So what is the problem with a little - or perhaps a lot :-) - of water coming down the compressed air line along with the compressed air?
A simple answer may be that it depends on what you are using the compressed air for.
The more complex answer follows.
For most applications, water blowing out the end of the air line with the compressed air is a problem.
If you are an air-brush painter, a micro-globule of water will land on your artwork, and prevent the paint from adhering to the surface. You end up with a fish-eye, or a lot of them, depending on how much water your compressor is generating.
Further, compressing air generates higher than normal water vapour content in the compressed air. When this air reaches a cool surface, the water vapour condenses into free water, making even more fish-eyes.
Air brush painters really have to get all the moisture out of their compressed air, both free flowing water and water vapour. For tips on how to do this visit ABOUT-air-compressors.com for much more information.
A lot of us do-it-yourselfers use compressed air to run air tools in our garages. The water in your compressed air will certainly coat the inside of the tool, and in time, rust it out. The life expectancy of the tool will be dramatically reduced when there is an air/water mixture running through the air tool.
Water will mix with your lubricating oil that you should be sending, with the air, through the tool. The water makes a sludge mix with the oil and any airborne debris (dust etc.) that comes with the compressed air. Then, when this sludge dries out between tool uses, the result might actually prevent the tool from working at all the next time you go to use it.
Hint: If the tool will not work when you are supplying enough air at the correct air pressure to run it (do please check these first) then sometimes a gentle tapping of the tool housing with a hammer might loosen up the vanes and allow the tool to run again. If this occurs, then once it's working again, flood the inside of the tool with lubricating oil through the air connection, and run it into a bucket until all the oil has blown through. This may clean it sufficiently to allow it to run again next time you want to use it. Failing that, it's time to take the tool to the shop for a stripping and cleaning, if you are not up to doing that yourself.
A few home compressed-air users may have built devices for their home or garage that use air valves and air cylinders to make them work.
Water flowing down with the compressed air will act negatively on both the air valves and the air cylinders.
With manual air valves the sticking can be overcome by exerting a bit more force on the valve handle. Not so with solenoid valves. These electrical devices shift the valve inernally with a magnetic coil or with pilot-air, and if the valve is full of gunk that came from the compressed air, it likely won't work when you want it to. Once again, may I suggest a gentle tapping, the failure of which will mean either stripping and cleaning the valve or replacing it.
Air cylinders come from the factory with permanent lubrication. Read "permanent" as lasting a long while, not forever. Regardless of how you define permanent, know that the factory lubrication will not last as long if you have water running in and out of the cylinder as it cycles. Eventually all factory lubrication will be gone, and excessive cylinder wear will result.
Do you care if you have water in your compressed air? For the life expectancy and operation of your compressed air devices, I think you should!