What bind-on-equip items exist in Diablo III, if any?

Solution 1:

The concept of bind-on-equip doesn't exist in Diablo III. Bashiok said something about it here (scroll down to his post):

Yeah, we realized that binding is kind of a crappy way to pull items out of the economy. If you say that the average player produces 100 items an hour and maybe gets 1 upgrade in that time, then binding at best can account for removing 1% of items from the economy. And that's being very generous at high levels.

Binding isn't really substantial in making a viable economy, but it is really good at establishing item prestige. Which is how it's used in WoW.

We expect salvaging to be compelling enough to remove a good percentage of the most valuable items from the economy. High end components obtained from salvaging high end items are needed for high end crafting and enhancement.

We're not promising anything on patch content, but we also feel that keeping up on introducing new items consistently will keep it from being possible for a glut of the best items from building as 'the best' can be a constantly moving target.

Courtesy of Krazer (in the comments):

Jay Wilson: I’m happy to announce that we recently decided there will be no binding of items in Diablo III. They will be freely traded for the life of the item. The only way we are going to do any kind of binding would be for things that are not progression-sensitive. Like we might say…a quest item. We don’t want you to be able to give to other player to short circuit a quest, but if you find a sword, piece of armor, or gem….anything that you find in the ground, once you pick it up, you can freely trade it…forever.

Solution 2:

The Blizzard FAQ on the Diablo 3 auction house addresses this under the question "If I no longer need an item I bought in the auction house, can I relist it in the auction house?"

Answer:

Yes. Once you've purchased an item and sent it to your stash, you can do anything with it that you could if you had acquired it through your own adventures. You're free to use it yourself, or trade it to another character or relist it in either the gold-based or real-money auction house. In fact, you can generally do any combination of these things -- for example, you can purchase an item in the auction house, use it for a while, and then relist it or trade it to another character. Aside from certain quest items, there will be very few (if any) items that will be "soulbound" to your character and therefore untradable.

Solution 3:

Previous answers are now out of date. First of all, there are no quest items: They're referred to, but they never actually show up in your inventory. Second, and more importantly, while there are still no bind-on-equip items, there are a handful of bind-on-pickup items. Specifically, the Staff of Herding, the Hellfire Ring, and all of the materials involved in making either, are all bind-on-pickup, and so can never be traded or auctioned.