They're great. I had a 2004 which I just traded in for a 2011 Buick Enclave. I was (or so I thought) over the minivan stage and our Odyssey had 145,000 miles and Buick had 0%APR.
Things I miss about my van:
automatic sliding back doors, great for kids
smooth ride, even at 145k miles
great gas mileage 22city/26highway, even at 145k miles and took 87 octane!
leather upholstery was very high quality and didn't have one tear or thinning area
the space, the space, the space - I could fit more into that back area, with the 3rd row recessed, than my DH could fit into the back of his short-bed pick-up
DVD player, never had one problem and was played constantly
reliabiltiy - it never broke down, not once
cheap oil changes, my Buick's oil changes are 2x more
cheap tires
What I don't miss:
It was terrible in the snow. I think this is a class issue as most minivans are bad in snow. I've been told the Toyota minivan has AWD, but I never looked into this so I don't know for sure.
In comparison, my Buick's interior leather and carpet is cheap, cheap, cheap. The leather is already showing wear and deep creases and we've only had the car since December. The carpet and plastic that make up the rest of the interior is also cheap. There are some deep scratches from my kids shoes, on the back of the driver's seat. The leather on the seats doesn't extend to the entire seat, it just covers the top. The rest of the seat is covered by fabric/plastic...not like my van which had all leather, except for the back which was a much better material than my Enclave.
And although the Buick has a better 3rd row than most SUV-crossovers, it's still not nearly as comfortable as the van's 3rd row.
Minivans are not cool. They will never be cool and my current mid-life "situation" requires I feel cool. So, I won't have another minivan, but if I had very young kids, I'd have one in a heartbeat and I wouldn't hesitate to get an Odyssey.