Practically everything that can be put in the Auction House will give you some money back.
You can try your chance at gray items - I've seen and heard of people that have had good luck selling a few select gray items for RP purposes, collecting or just for fun. But in general, I'd leave grays alone.
As for the rest, there's 99.99% chance that it can be used in the Auction House.
What can be profitable depends of your server's economy and the status of the item in the World of Warcraft.
As items appear and disappear in the game, the demand of certain items changes as the players' needs change.
And, of course, the gold-maker has to be one step ahead of players' needs.
You find yourself with items in your inventory and you don't know what to do with them ?
Wowhead is your friend.
It'll tell you if it's an item for a quest, for a crafted item, if it's needed in a tradeskill, and you'll have player comments (which can be a good indication of the marketability).
Now that you know what it's good for, you can hit the Auction House and see what's happening to that item: if it's selling well, if there's none if it, if you get more money back from crafting whatever it's being used for, if you could make a profit by buying all of the listed items and resell them, etc.
And sometimes there's no way to make a profit - it's just best to vendor some of them or to stockpile them until the stars align and the time is right.
My point is: destroying items is a waste of time because every copper counts and there are many possibilities for items before you should be considering the vendor option.
Pointing back to the post I wrote: the slightest profit can be worthwhile if you have the knowledge of the item, coupled with the right timing and a bit of luck, and if you're using the right tools (which I will go on about in a future post).
I know - this post feels like it's stating something that is obvious but I've discovered that for many people it's not. Just getting to the step of browsing the item on Wowhead is usually too much for many people. And that's how knowledge makes you win.
Because many people will only look for certain items when they have a need for them.
And because you know what they need, you'll be there to supply the items.
And sometimes, the items they they need are the ones they've been selling straight to the vendor.