Some persons in this thread regard the radiation dose of a CT scan as negligible.
This is certainly not true. CT scans make up for most of the diagnostic medical radiation dose in the general population and the dose received in one CT is -depending on the scan - equivalent to several years of natural radiation dose. Already now the dose due to medical examinations in industrialized countries is higher than the natural radiation and this is mainly due to CT examinations.
The general rule in radiation protection is called "ALARA", "as low as reasonably achievable" whence at least I would avoid a CT if alternative techniques are available.
Furthermore, to detect a damage in soft tissue, MRT is usually preferable.
The German Federal Office for Radiation Protection has a nice brochure on radiation burden of medical examinations. Although it is in German, the diagrams may be informative to non-German speakers, too:
http://www.bfs.de/en/bfs/publikationen/broschueren/ionisierende_strahlung/medizin/STTH_Roentgen.pdf
There's also a similar but shorter text in English:
http://www.bfs.de/en/bfs/publikationen/broschueren/ionisierende_strahlung/medizin/BRO_Roentgen_Nutzen_und_Risiko_eng.pdf
You can see that in particular CT scans of the abdomen go in hand with quite high doses of 8 to 20
mSv.