Two separate issues are at work here. Ionizing radiation will cause damage to cells no matter the power level (however, at very low power levels such as the normal background radiation the damage is likely negligible).
Non-ionizing radiation such as microwaves produces heating effects. At low power you may perceive warming and nothing else, at high power you'll surely be burned.
Heating from microwaves can be more damaging than say heat from a stove because the longer wavelength means heating starts from one's insides and will cause considerable tissue/organ damage before one realizes what's happening.
Microwave ovens can be very dangerous if the door interlocks are bypassed and the door opened whilst it's operating. People who are seen on YouTube doing this are either ignorant of the dangers or are just plain crazy!
Microwaves, especially shorter wavelengths above 5GHz (that's about 5 times that of mobile phones) are especially damaging to the eyes as interior of the eye doesn't have a good way of dissipating heat.
I was taught never to look into waveguides even when only used with receiving equipment as even the local oscillator can have enough power to damage one's eyes if concentrated in a small area. About 1W/cm^2 has a noticeable heating effect and from about 5GHz (approx 6cm wavelength) the CSA of waveguides is small enough to concentrate EM radiation of, say, 1W to do damage to one's eyes.
For mobile phones scale that figure down as the longer wavelength dissipates the power over a greater area (also remember area goes up by the square of the wavelength which means that phone wavelengths are much less damaging than microwave frequencies (>3GHz).
I'm not up to date on the latest research but from what I was taught I'd be concerned if more than 0.1W/cm^2 were entering my eyeball. In fact, if I recall the Russian standard for exposure was 0.1W/cm^2 which was considerably tighter than the US figure of 1W/cm^2.
Keep in mind those figures were for the microwave band which starts at 3GHz. As mentioned, because of the longer wavelength of mobile phones it's unlikely one could exceed those figures whilst using a mobile.