Please be aware that MRIs have an utterly massive amount of radiation. X-rays are almost always done first because of the risk of damage from the radiation. You really don't want to have an elective MRI. (That said, I'm aware of no known studies that have demonstrated long-term risk from MRI radiation, but to me, prudence says you don't subject yourself to an MRI that you don't have to.)
The 'radiation' involved in an MRI is electro-magnetic radiation, otherwise known as radio waves. It's true that the field strengths involved are thousands of times stronger than what you encounter in everyday life but they are by no means harmful the way that ionizing particle radiation (X-rays, gammra rays, etc) is...
The most likely side effect is peripheral nerve stimulation and even that highly unlikely because the field strengths are controlled to avoid it...
In general MRIs are perfectly harmless and don't have any serious or lasting side-effects.
X-rays and Gamma rays are "only" electro-magentic radiation too. As are microwaves, and most people wouldn't place their heads into a running microwave oven.
I'm not saying that the radiation used in MRI would be harmful, but saying that its harmless because it's electro-magnetic is just plain wrong.
Perfectly true, I phrased my comment the way I did to get away from the idea that 'all radiation is bad'. EM radiation can be dangerous in that it can cook you if there's too much of it... However it's far less likely to cause the serious tissue and genetic damage that particle radiation would.
I would gladly put my hand in a microwave before I would be willing to bathed in gamma rays...
An MRI below about 5-6 teslas is perfectly safe provided there is no ferrous shrapnel in your body. If there is shrapnel in your body, the magnet will pull it out and cut your body in the process.
(The X-ray is done to make sure you don't have any shrapnel and also because it is cheaper. If the X-ray reveals the problem, you can avoid the more expensive MRI.)
RF radiation will only harm the human body at very high field strengths (think microwave oven). The typical medical machine only gets 1-3 teslas, though a few research machines can reach the 6-8 tesla neighborhood (e.g., Dan Sodickson has an 8 tesla machine here at NYU).
One of the main reasons to do the X-ray first is to ensure that you don't have any unknown ferrous metal (from welding, grinding, etc) that will become a projectile under the intense magnetic fields.
(I wasn't aware that there was a massive amount of radiation from MRIs, and tend to doubt that claim. Are you confusing it with CT perhaps?)
1) It's radio energy, not the ionizing radiation that we associate mutations and cancer.
2) It's actually very low power. Most of the energy in an MRI machine goes toward maintaining a super-high magnetic field. The radio energy used is on the order of a few watts per kg body weight.
3) The danger isn't being irradiated. The danger is being cooked.
