Any gold card perks?
Solution 1:
The only differences between a gold card and a regular card are its appearance and dust costs (for expert set cards). Gold cards that create other cards will create the gold version- a gold mind vision will create gold copies for example- but again this effect is purely cosmetic.
Using an entirely gold deck will get you a golden coin when you go second, instead of the regular coin.
Aside from looking cool, gold cards can be useful in deck testing. Using a gold copy and a regular copy of a card allows you to tell which copy is which. If you keep track of how often you see the gold one, you get an idea of how often you'd draw that card if you only had one copy in your deck.
Solution 2:
The argument has been made that gold cards could actually hurt you in the case where you have a golden card and a non golden card of the same card in a deck. If your opponent thought steals you and sees one of them, then you played the other, they now know you have another of that card in your deck.
Solution 3:
Other than looking cool, Golden cards hold no benefit.
They are however worth significantly more if you want to turn them into dust
Solution 4:
Just adding to another good answers, looking Golden Soulbounded cards can tell you an estimate of opponent level. By example, if your opponent has a Golden StormWind Champion, your opponent is level 59/60 with Paladin class!
http://hearthstone.gamepedia.com/Paladin#Level_11-60