Attacks show enchanted particles without enchanted weapons

Those are just knockback particles.

Confirmed.

It should be noted that this isn't just a visual effect. You actually deal double-damage: you can kill a zombie, skeleton, or villager in just 10 unarmed punches.

It's fixed in singleplayer, but not multiplayer.

I was on a 13w36b server last night and I noticed this. I tried it in singleplayer just now and it's fixed there.

Your server is likely not updated to the latest snapshot.

@Dinnerbone

It's not my server, it's my friend's.
I went on there just now, and he said it's on 13w36b. Then I punched a cow and saw the enchantment particles.

Oh wait, you were right, Dinnerbone.
On Thursday, when 13w37a was released, I viewed my multiplayer screen while in that snapshot. His server wasn't updated, so I was able to see the version number. It was still on 13w36a! I didn't know "b" version clients were compatible with "a" version servers.