I've had a minivan for 7+ years and love it. I plan on keeping it until my kids are in college and then having a small car (ala Honda Fit) as my primary vehicle. I don't really like larger vehicles, but the Honda drives like a sedan - the only gotcha is that you do have more blind spots and need more space for changing lanes etc.- i.e., you need to be more cautious which can be difficult with kids in the car. I will likely keep my minivan for roadtrips and larger shopping trips, as well as when visitors are in town. I would guess it is going to last me for 200,000 + miles.
That all said, I did not get a minivan until my kids were in elementary school as you really don't need that much space unless you plan on lots of roadtrips, as you don't do major carpooling typically in the early years.
However, for roadtrips vans are fantastic. We take out seats (a must for flexibility in minivans and have lots of room for the kids stuff, coolers, etc. Of course, kids are also belted up. But, the van is great if you encounter bad weather as you don't have to leave the car for a picnic, etc.
I have also driven a truck and don't like it at all - the handling is different and maneuverabilty is far more limited. I've also ridden in larger SUVs and I know my minivan has far more flexible space and is far better.
We have hauled room fulls of Ikea furniture in my minivan due to the ability to fold the rear seat down without removing it - another MUST for ultimate flexibility.
The only plus for a minivan in the early years is the automatic doors and some ease in putting kids in/out (as compared to a sedan).
The minivans now are tons more flexible than more with lots more features, so I wouldn't hesitate to buy one. The only reason I haven't traded up is because I have had so few problems with my minivan (105,000 right now) - it's been in the shop once for something other than routine maintenance (another reason I prefer Hondas - they're superior in reliability).
In terms of safety, most minivans do quite well in the crash tests. Honda I think is the best - at least it was when I bought mine).