5:09 p.m. on October 7, 2012 (EDT)
In the 6+ decades I have been in the woods and hills, from car camping at the trailhead to backpacking to major expeditions, I have witnessed a couple dozen (maybe more, since I haven't kept a notebook on the topic) stove incidents. Most were integral-tank stoves (such as the Svea 123 type, but including Coleman Peak 1 and other brands, and butane canisters of the old Bleuet "puncture cartridge" type and the screw-on type, such as Jetboil, Primus, Coleman, and others make). Several were what Erich describes (oversize pots reflecting the heat and/or tight windshields that reflected heat onto the fuel tank or canister). Two of those produced shrapnel that landed some distance away (including a couple pieces that embedded in nearby tree trunks and one injury). One involved a professional climbing guide on an expedition who wanted to speed up the cooking by setting 3 XGKs with their burners together and the windscreens clustered around the pot, unfortunately including the plastic pump end of one of the fuel bottles inside the windscreen. The image below shows the stove and fuel bottle after they were heaved out of the cook tent into the snow.

One incident, during a winter camping course for Boy Scout adult leaders, happened when the stove owner had improvised a windshield from a large coffee can and set the Coleman Peak 1 inside his "windscreen". Another that I witnessed in the former Biolet Campground in Chamonix (France) involved a couple of Irish lads who decided to make a brew (tea) after a late night at the Bar Nacionale. I didn't witness the first part, but ran over after the yelling started. They were sitting in the door of their small tent (one door only) when the relief valve let loose, igniting a huge jet of flame (much more than my height by the time I got there). Since their tent had no back exit, they felt trapped. Luckily one of the other climbers was a skilled futbol player and booted the flaming stove over into the grass (we had had a huge rainstorm that afternoon, so everything was well soaked).
Probably the most famous stove incident is the one described in the book "The Hall of the Mountain King" by Howard Snyder, concerning the disastrous 1967 Wilcox McKinley Expedition. At one point, the entire group are in their cook tent when one of the stoves runs out of fuel. They were using the Optimus "suitcase" stoves, modified to reduce their weight. They proceeded to refuel the empty stove while the second stove was still burning. According to the book, this triggered an explosion/ignition of the fumes. The tent, a sleeping bag, a couple of parkas, and other gear vanished within 10 seconds (one of the expedition members said he had leaped for the tent entrance and by the time he got there, the entire tent was gone). Wilcox subsequently published a "Reader's Guide" to the Snyder book, intended to be "point by point rebuttal". Regardless, 7 of the original 12 members of the expedition perished, with 6 of the bodies remaining under the snow somewhere on the "Football Field" just below the summit.
And, of course there are the many carbon monoxide poisoning incidents, including Admiral Byrd, who was rescued just in time before he died from using his stove in a small, tightly sealed hut in Antarctica.
As Erich implies, "operator error" is involved in the vast majority of stove incidents. As far as I remember, it was the sole or primary cause in every incident I have witnessed. In one or two of the cases, it was poor maintenance. But the rest were "operator error" - carelessness, or sometimes just plain "dumbness". Hmmmm ... "poor maintenance" is "operator error", too, when you think about it.
On the other hand, Barb and I have had our 2 Sveas and the very similar Primus 71L since the middle 1960s (1959 for the Primus 71L), and they still work just fine. They have had a few parts replaced (O-rings) over the years. We do use others of our 30-some stoves more these days (XGK-EX mostly and sometimes the Jetboil Helios).
As a friend of mine, Clyde Soles, wrote in an article on stoves in Rock and Ice Magazine a number of years ago, "Treat all stoves like the barely controlled explosions they are."