Yes -- for the most part. Keep in mind that you are receiving an intake of caffeine from additional sources throughout the day as well (such as from soda or chocolate), so it's important not to overdo it on the coffee. By "overdo it," we mean refilling pots of coffee per day, not necessarily a few cups -- so, generally, you most likely are consuming an appropriate amount that shouldn't negatively affect your health.
In fact, coffee may have unique health benefits. According to many recent studies, caffeine may reduce the chances of developing diabetes, heart attacks and strokes in individuals who don't have a predisposition to these ailments. Plus, caffeine is especially good for your mind's health due to its interaction with the chemicals in your brain. That's because your brain translates caffeine as another chemical called "adenosine." Adenosine is what causes us to feel tired -- alerting our body that it's time for sleep as it builds up throughout the day. Since caffeine can disguise as adenosine, it can attach to the adenosine receptors in your brain, which typically makes you tired; however, in this case, caffeine has the opposite effect. Caffeine causes us to feel awake, alert and focused. By training our brain to focus more often, studies have found that this may reduce the chances of developing Alzheimer's disease, dementia and overall memory loss later in life.
So, unless you have a medical condition that requires limiting a stimulant like caffeine, feel free to enjoy your java fix -- just try capping your indulgence to a cup or two a day.