Apple Watches offer health-tracking features, including heart rhythm measurements through ECG (typically measured by attaching several electrodes) and Peripheral oxygen saturation of the blood (SpO2) (typically measured at a fingertip using a pulse oximeter). This is not classified as medical-grade, and has very limited accuracy or reliability (see here for SpO2, here or here). It may even be annoying if it tells people they may have a problem when there is no actual concern or, in rare cases, it could be dangerous if it falsely gives people a sense of security, for example by reporting a fairly normal level of oxygen while in fact your oxygen is too low.

Abbott provides continuous glucose monitoring (CGM) with their FreeStyle Libre 2 and 3 systems. A specific sensor is attached to the body for a period of about 2 weeks and it connects with either a smartphone or a handheld display. This replaces the typical blood glucose monitoring devices that include use of a lancet to prick your finger, such as here.
Omron makes blood pressure measurement devices that rely on cuff-based designs that automatically pressurize and measure at set intervals. These are used mostly to watch out for hypertension, which is a big health risk. Wrist-cuff devices are expected to cause less discomfort and muscle compression than traditional upper arm cuffs. These are fairly reliable (here).
Withings sells beautiful watches with a range of health sensors for ECG (“detect a potential cardiac anomaly and get a cardiovascular assessment in 30 seconds”), blood oxygen levels and body temperature. They also sell arm-cuff-based systems that combine BP, ECG and stethoscope (here). As a side note, they also have a good sleep analyzer in the form of a thin strip under a mattress.
iHealthLabs has several devices like the iHealth Push Wrist Blood Pressure Monitor, and the iHealth Air Pulse Oximeter, and their fancy scale, the iHealth Nexus Pro Wireless Body Composition Scale that can do an ECG as well. Not really wearables, but nice stuff.
BioIntelliSense has an FDA-cleared BioButton monitors temperature and heart rate and respiration, both at rest.
BioSensics has a device that measures Upper Limb health, called PamSys ULM.