Coffee is both good and bad depending on who you are. If you have asthma, coffee can actually prevent you from having an attack because the caffine acts as a stimulant which increases the flow of blood and in turn the flow of oxygen within your blood stream.
Adversely, as hinted on before, it's about as good for the brain as taking a steal spike and driving it in your forehead. Coffee can cause hardening of fatty cells within the brain causing memory loss and the early onset of ahlzeimer's disease. It also damages the brain (as does soda, tea, and other caffine based products) by blocking the adenosine receptors which can cause irregular heart rythms and poor circulation, as well as reduces your ability to fight off contagious disease.
Now, remember that bit I said about harding fatty cells and loss of memory... well there is an adverse study recently put out that states that this might just be your long term memory, as coffee has been shown in lab tests to cause hyperactivity in the prefrontal lobe which actually increases your short term 'executive' memory which is in charge of things like attention, concentration, planning and monitoring.
All that being said, if you are having an asthma attack and you don't have a visteral/steroidal inhaler around, drink yourself three cups of coffee it'll clear that attack right up. But if you have a history of alhziemers in your family I would suggest you avoid caffine products all together. Otherwise, a cup or two a day won't kill you and might actually make you more attentive and increase your ability to make wise decisions on the margin.