Basic Taxonomy

I'm not sure when the trend of giving dragons the wrong number of legs started, but I think the first time I noticed it was in 2002's Reign of Fire. It's clear people have been getting it wrong for much longer than that, though.

Reign of Fire getting it wrong was annoying; Harry Potter getting it wrong was upsetting (despite this); but Skyrim getting it wrong was the absolute last straw. Over the last decade it's become standard to show dragons as two-legged creatures crawling on their wings like pterodactyls. But that's not a dragon! Dragons are six-limbed, flying, firebreathing lizards; in that order! You can take the fire away - you can even take the flying away (but keep the wings) - but the minute you take away a pair of limbs, it's not a dragon. It's a wyvern.
That's not a loose rule, either. Sure, dragons don't exist, but neither do centaurs; and no-one would ever draw a centaur with two legs. Or a gryphon. Or an oliphaunt.
Fantasy has its natural laws, too.

If December rolls round, and I see less than six limbs on Smaug, there will be hell to pay. This gives me hope

Ducks with four legs are cute as anything, though. I want one!