I've recently seen a few new smartphone apps dedicated to your health. In the past, I've seen things like Runkeeper that help you keep track of your fitness. More recently, I've seen things like this: an iPhone add-on that can measure and monitory your blood pressure. The iHealth dock is even capable of taking that information and sending it directly to your doctor. They have plans to expand to support various other monitors (like glucose monitors).
I think that making these sorts of checks less scary is a great idea. Being able to do this sort of stuff at home, using a device that you are already comfortable with, will certainly lower the anxiety associated with going to a hospital. It can simplify doing these checks, and increase accuracy by preventing things like the white-coat effect.
I'm not sure about this whole "sending data to your doctor" thing, though. I don't think healthcare providers have time to log every single blood pressure reading you take, nor do they really care. Your day-to-day blood pressure fluctuation is not that important. They really care about things like averages. This is something you can do on your own, and then just submit an average to the physician. As I'm learning at Karos Health, healthcare providers already have enough problems organizing all the available data in a secure and accessible way. Having random iPhone data thrown at them is only going to complicate the situation. While self-reporting is generally a good idea, it needs to be implemented very carefully to be effective.
In any case, I would like to see what other ways smartphones can make healthcare more accessible.