There have been incidents with nuclear subs, but few due to problems with the nuclear part of them, and none at all in close to 30 years. The Thresher imploded in 1963 while doing tests to see how far it was possible to dive (answer: whoops, not that far). The Scorpion was lost in 1968 under circumstances that were initially mysterious, but subsequent investigations conclude that a torpedo malfunction was probably the cause. Those were the only two subs that were ever lost, and neither loss had anything to do with its power plant.
A brief list of problems with subs and other nuclear reactors can be found here. There are quite a few incidents that make this list only by association; i.e.: it’s a conventional accident that just happens to involve a nuke in some way. The guy who made the site presents these as a record of nuclear power’s record of a lack of safety, but I’d bet that a similar accident list for many other kinds of power plants would show problems that are as bad or worse.
I found an article about the radioactivity that coal power-plants release into the atmosphere, along with some discussion of other environmental considerations in relation to nuclear power. In short, you’ll have a better chance of “glowing in the dark” if you live close to a coal plant than if you live close to a nuclear one. I believe I found and bookmarked that piece after reading an article about nuclear power that I read earlier this year, written by a Greenie, Patrick Moore, who is in favor of nuclear power now though he opposed it in the past.
I think we’ve done threads before on nuclear power. There’s a big thread here where several people, notably Stranger On A Train, give a lot of information about nuclear benefits and difficulties. Lots of info there and seeds to do your own research if you’re interested.