Here's a medical oriented project: DIY ECG Machine. The project write-up goes through the machine that he's built and gives you some guidance towards building your own. For anyone who is new to the medical field, this is some really cool stuff.
With perhaps a more noble cause in mind, other than just for fun, here is the electronic stethoscope. The build isn't as complex as it might seem and the project write-up offers a deatiled guide for reproducing this device. There's also much background information all for you.