Paint drops. I've gotten a couple of cans.
Black & White paint are only available from crates (and could be bought from the store for a limited time during a special sale).
Also, some hats have been purchase-only or crate-only, hats with really rare special particle effects only come from crates (I think), and the demoman's haunted Halloween axe doesn't drop (but it's functionally the same as the eyelander, without a taunt). Oh, and the practice versions of the rocket and sticky launchers may be store-only, I'm not sure about those.
It can be a pain to get specific items via random drop, though. I'm still waiting on getting the ingredients necessary to make the two new medic weapons.
You can idle for weapon drops by starting a local practice game against bots, and then spectating that. If you're connected to steam while you spectate, you'll get drops (though you'll have to die or go to the in-game store for them to actually appear in your backpack.) Each week has 11 hours of gameplay that will produce drops (with some roll-over from the previous week) after that time is up you won't get any more drops until the drop cap resets on Wednesday evening (5pm PST).
EDIT: If you think that TF2 has changed, you should see what they've done with the open beta. They're trying an experiement where characters all have double health (900 health for an overhealed heavy.) and buildings take 50% -less damage. It takes a lot longer to kill anything. Spies are super annoying because only backstabs are still instant kill, and they can often run away without dying, even after being detected.