Oh yes they did! Especially in the original game, not so much later, but electrocution was quite common when changing light bulbs - they just somehow didn't include it in later EPs, but any downloaded objects which were just for Sims1 and LL could still cause electrocution.
Also barbecue fires were quite common, and sims often got burned to death!
I had the "spontaneous combustion" bug, which was fixed by the first patch. Basically what happened was that a sim would die in a cooking-related accident, but for some reason wouldn't appear as dead. So you could go on playing as normal, unknowing that actually the game thought he was dead. Then, a few sim hours or days later, the sim would "have a fit" (literally - it looked like some kind of seizure) and die, with no warning.Also barbecue fires were quite common, and sims often got burned to death!
I was significantly traumatised by this to be unable to sleep, and my dear partner ended up staying awake until 5am downloading the patch (28.8k dialup - fast, at the time) to fix the bug, and SimEdit to fix the token that made the game think Jim was dead.