Korean Air have lost four 747s - one undershot at Seoul in 1980, one was shot down in 1983, one undershot at Guam in 1998, and one rolled over and crashed after taking off from London (STN) due to a failed instrument. A further 747 landed but was declared a write-off after pieces of the trailing edge flaps detached and struck the fuselage. They also lost at least two 707s, one shot down in 1980 and one sabotaged in the early 80s. And a couple of A300s in landing accidents, and an MD80.
An Aussie mate knew I collect airline cutlery and flew Korean Air to London. He brought me (I should say 'stole') a few items off the various meal services he enjoyed. A pilot friend of mine who knows what goes on at Korean Air saw the items in question and was moved to remark, "I didn't know anyone had ever lived to collect the full set!" I wouldn't go near them if I were you.
BTW, Asiana have an excellent safety record, and since they have profited so much from Korean Air's woes, I think it is more in their interest than most to remain a 'safe' airline. I think they pranged a 737-400 but that's all. Having said that, they have a smaller fleet and they've been around a lot less that KE. But they're supposed to be good and I know their insurance premiums are about half KE's, according to a friend of mine in the reinsurance business.
fly Saha Air 707s daily from Tehran's downtown Mehrabad to Mashhad, Kish Island and Ahwaz