Goose got a brain tumor, an intern got stabbed, one was in Iraq and got busted by a roadside bomb, and a helicopter fell on another guy (during a rather satirical episode). That's about it, but at the times those characters died they were pretty important to the plot. Add in Carter's drug habit, a crazy Sally Field, Johny Legs pissin' on cops, another fellow losing his legs etc, etc. The show was far from conventional, it wasn't afraid to take risks and delve from it's "path". Unlike other shows they made a point to pick incidents that actually happened.
We all know 4 doctors dying in 15 years is probably unrealistic. Yes, but this isn't a documentary, it's merely a show based on reality. Think of it as a modern MASH. Throughout it's run it gave us the serious, the funny, the sad, the satire... a variation of writing few shows have been able to master. Which is why the show lasted so long even though star after star past through it's ranks, in my opinion the show probably had a few more years but chose to do the the classy thing by going out on top.
Add to that the guest spots done by fantastic actors such as Danny Glover, Sally Field, Mickey Rooney, Ewan McGregor, Alan Alda, Forrest Whitacker, that's just all I can name off the top of my head. And we might have witnessed one of the best shows television has given us ever.