The direct experience that I have is, as I mentioned somewhere, a decade-and-a-half old, but I was speaking of unionized work in the electrical trade.
As far as benefits go, they were indeed very good. As has been mentioned around here, these jobs tend to be somewhat more physically demanding than the average programming / desk jockey position, and the result of that was better than average health insurance. The insurance industry everywhere has changed a lot in the past decade, so I'd recommend doing your own research.
For perspective, my cousin got Lyme disease, and didn't catch it until well after he'd been symptomatic. He was a drummer in a band, had thick, long hair, and had a tick on his scalp that went unnoticed. When he first began acting erratically, his parents chalked it up to typical teenage rebellion. He drove a car into the house and didn't realize it, ran another car into a telephone pole, and basically got to 'late-stage' symptoms before it was inspected.
He spent months in the hospital, specialists were flown in, and ultimately, he was made better -- though later in life he's developed early arthritis, which is believed to have been caused by the Lyme. All totalled though, nobody was bankrupted by the medical treatment and cost of the rather excessive care involved.
As for job stability, there are indeed periods of boom and bust. Boom periods often involve working optional overtime, which is compensated as overtime -- nobody in a union works off the clock. When I was a member, I never had a day where I missed work due to lack of employment, but I know that it does happen. I can't speak for how frequently it is from experience, but the union hall makes an effort to keep everyone as employed as they're able. In an up economy, this likely means steady work, in a down economy, I don't know.
Anyway, if you have any other questions, feel free to email me (contact in my profile), and I'll answer what questions I'm able. The (again) disclaimer is that my experience is dated, and a lot has happened since then, but as most of my family back home are tradesmen, I can ask around for answers if need be.