I believe that an exercise bike can be an excellent investment into your health and wellbeing. I actually purchased one for my family not too long ago because they would rather exercise at home than join a gym.
They aren't too expensive and can be very effective for increasing your level of fitness, improving your health and assisting fat loss. The beauty about a home exercise bike is that they are easy to use, convenient, comfortable (so long as you have a well-padded seat lol) and effective.
When choosing a piece of cardiovascular exercise equipment, one of the most important factors is to consider what you will enjoy using most. Some people hate treadmills, others dislike bikes - it's ultimately a personal thing. At the end of the day, if you don't enjoy using it, there's not much point in making the purchase.
With regards to the effectiveness of an exercise bike (or nearly any machine for that matter), it is only as effective as the level of effort you invest into your exercise. This includes factors such as the amount of time and exertion/intensity. If you enjoy using the machine, you will most likely yield far better results than any other machine.
Speaking personally, the only cardio machine that I really use is the exercise bike - because it's fun (well at least I think so :P).