when it comes to diagnostic x-rays, the main driver is a risk vs benefit determination by the clinician. Does the clinical information derived from an x-ray study exceed the small increased risk of developing a cancer 20 years or so down the road? A commonly quoted value for the number of excess cancers due to radiation exposure is 0.0001 per Sievert (Sv) (1 excess cancer in 10000 people per Sv). The topic of 'harm' from x-rays is pretty subjective and prone to significant debate, because for normal routine exposures (even repeated exposure), any potential 'harm' is stochastic in nature and generally not manifested until many years down the road.
Digital x-ray detectors based on flat panel transistor arrays are getting more widespread, but there's only so much you can reduce the amount of radiation required before you run into problems with noise that affects image quality.
MRI can be the primary imaging modality for certain conditions, but is unlikely to replace most routine radiographic procedures because it's expensive and slow. Likewise for CT for being expensive and involving much higher radiation exposures.
Despite the technology, reduction in radiation exposure boils down to technologist and radiologist education. You can give them the latest and greatest technology, but if they insist on using techniques they developed for film/screen systems they're not taking advantage of anything.
There is a lot of work that goes into developing optimum x-ray techniques that provide the best image quality for the lowest radiation dose. A lot of it depends on the anatomy being imaged, the equipment being used and the radiologist doing the reading. Techs and radiologists need to be educated about the technology they're using so that they can develop optimized x-ray techniques.