Here are some Trait ideas I had since I was introduced to the new mechanic. Most of these predate the Weekly Design Contest about this topic, so there might be some overlap (I am writing this while the contest is still going, but am not going to publish it yet, in case someone wants to submit similar ideas). In general, I think it's surprisingly difficult to create a well designed Trait which is interesting in most games. Here is what I came up with:
Blessed
When you gain a Blessed card, take a Boon. Receive it now or at the start of your next turn.
Simple and quite obvious, I admit.
Sprawling
Trait
When you discard a Sprawling card from play, gain a Sprawling card.
Might be too swingy, but I like the premise.
Elegant
Trait
When you gain an Elegant card, +1 Action, and if it's your Buy phase return to your Action phase.
Donald X. lists some Village type Trait ideas in the Secret History, but no Villa variant.
Ducal
Trait
In games using this, Duchies are also Actions with "+2 cards, you may play a Ducal card from your hand."
An attempt to make early Duchies a little bit more interesting.
Fleeting
Trait
When you discard a Fleeting card from play, exchange it for a card with a different name costing up to 
more.
Somehow the child of Butterfly and Reckless. I like it.
Hopeful
Trait
After playing a Hopeful card, if you have exactly 7 cards in play, gain a Wish.
Let's hope we find a Leprechaun at the end of the rainbow ...
Independent
Trait
After playing your 3rd Action card in a turn, play an Independent card from the supply, leaving it there.
This might be my favourite. It was my submission for the Weekly Design contest.
Persistent
Trait
When you trash a Persistent card, +2 cards, set it aside, and at the end of turn put it on the bottom of your deck.
The setting aside might be necessary to avoid loops.
Diplomatic
Trait
When you gain a Diplomatic card, +1 Favor.
When you trash a Diplomatic card, +3 Favors.
Diplomatic cards are also Liaisons.
After playing a few games with it, I changed the when-trash bonus from 2 to 3.
Sustentative
Trait
After your 1st shuffle: When you end your turn without having played a Sustentative card in it, discard down to 4 cards in hand.
This is my attempt of making a Gang-of-Pickpockets style Trait. I thought of a few different negative effects, but in the end I settled with the discarding (for the moment).
Educated
Trait
Setup: Move your +1 Card, +1 Action, +1 Buy, or +$1 token to this pile (when you play an Educated card, you first get that bonus). The first time you gain a Victory card, remove all your personal markers from Supply piles.
I haven't tested this one yet. At first it triggered only after buying a Victory card costing
or more, then I changed it to match Cage.
Bonus Ally:
Pirates' Den
Ally
At the start of your turn, you may spend 5 Favors to gain a Loot, or 6 Favors to gain a Loot to your hand.
What do you think?
