Minivans are still more likely to rollover than passenger cars, but suvs and pickups at the time of this article rollover in one in four accidents - which is shockingly high.
I don't really pay attention to cars that much, but while I see utility vans all the time, I rarely see a minivan nowadays.
But while minivans won't roll over, they also will almost certainly have longer stopping distances than a sedan.
They've really decreased in popularity. As far as I know there are only a handful of manufacturers even making minivans for the US market: Toyota, Kia, Chrysler, and Honda, and they each only offer a single model last I knew. I'm not sure why no one buys them anymore since from a practical standpoint they offer a lot more space and ergonomics when compared to most SUV's. My only guess in that people have a lot fewer kids these days.