In the Steam Auction, every Steam item (card, booster pack, background and emoticon) has a gem value, which is awarded when the item is "recycled" (user clicks the Turn into Gems...
button).
How is that gem value worked out?
Is there some sort of biasness for rare items? Valve-made items?
I've noticed that all the sale emoticons/backgrounds are worth 100 gems each, along with items from Valve games^, free-to-play games and sales, while all other games only reach a maximum of 80.
^CS:GO somehow fits this rule, but Half-Life 2 doesn't.
Best Answer
There seems to be a "complicated" way to do this. WARNING: The following might differ for some games and versions. This is an estimate by this wikia.
So to sum this up:
Only trading cards, emoticons, and backgrounds can be converted into gems
Emoticons and backgrounds that deals with Value will always be worth 100 gems.
The gem value of a emoticon/background is based on the number of the cards in its respective set times the gem value of normal cards then divided by two and finally rounded to the nearest multiple of 20.
The gem value of a foil card is 10x of its normal version
Formulas could be found in the wikia link above as well as more information. For cards: