Check out this godsend, the wristband ambulatory blood pressure monitor. Academics are already strongly recommending 24 ambulatory blood pressure to replace the single blood pressure measured by the traditional arm cuff, so it's likely that all future blood pressure monitors will be of this wearable shape. Generally blood pressure monitors are able to measure heart rate, as for blood oxygen, you need to use pulse oximeter to measure. This type of device is already very small in size, and it is easy to make it a wearable device. The problem is that the clinical significance of ambulatory oximetry is not very clear. No one cares, and it's useless to record it!
Another health indicator that's often measured by wearables is the electrocardiogram (ECG), which is usually connected wirelessly to a cell phone. This handsome guy below shows one such device.