I bought the '99 Odyssey in 2006. So far it's been good to us. This was not subject to a transmission recall. Knocking on wood.
Five-star crash rating, especially side impact. Didn't want a minivan but decided it was safest way to go for our kids. I hated it at first but now like it. I feel pretty safe in it, and it's good for hauling things as we fix up our house. (Middle-row seats can be removed from car.)
I'm sure Honda has improved this already, but the automatic doors are very slow (especially annoying when you forgot something inside and have to wait for it to close then wait for it to open), and the one on driver's side always sticks. No button to open rear/hatch door. Speakers only in front.