I think most of the discussion in this thread is pretty off-base, but I don't really see much point in getting into it. On the other hand, as someone who hosts tournaments I feel like I'm somewhat qualified to address this:
Possession creates enough unfortunate situations, now made more common because of Donate, that I view it as a card that should be banned in tournaments. The only other one is possibly Rebuild - since Donald has said himself he doesn't play with it. (In another category are the replaced cards from the base game and Intrigue.)
There's a list of cards I don't use for my tournaments for various reasons. Some of the reasons are due to IRL constraints that I don't really think people here care about, but some of the reasons have to do a little bit with competitive integrity. I ban the following cards due to a combination of them being unpopular and the idea that they can lead to unfortunate situations, especially in 3P games:
Pirate Ship (3P tournaments only)
Cutpurse (3P tournament only)
Some of these cards I have nothing against, personally, but what I don't want to happen is for someone to leave my tournaments all salty because they lost to some guy who collided Urchins when they didn't, or on some "stupid <card> board where no skill was involved." I don't think that the results of my tournaments are any more "valid" because I don't use these cards, but Dominion's competitive scene is small enough that I think how people feel when they play tournaments is more important than any of that other stuff.
I also allow people to stack their decks at the start of the game, simply because I don't want people mad that they lost to some guy who got a 5/2 on a board where that's really good; I fully realize that this is a relatively small part of the overall variance in Dominion but man does this make people feel better.
I think both online and IRL tournaments would benefit from focusing a bit more on this type of thing for the time being, at least until competitive Dominion becomes big enough that I can quit my day job and just do that for a living. I'm counting down the days.