So - I think we're going to be unlikely to put forth a formula that lets us explicitly indicate which ones are more or less luck dependent.
In my mind we have several different cases of luck:
1. Luck in ability to purchase the card because of its price
Prizes - The ultimate here - you can only gain them in very specific circumstances - and if your opponent does first, you can't gain it at all.
Possession - 6p is expensive. It's hard to reliably get early, and if you get it late - the value of your possession is reduced. As others have pointed out - this is mitigated if you go for possession in an engine deck - which is nice because your engine is more likely to play possession often. It is also more likely to have your opponent want to quit dominion.
Golem - 4p is also expensive. You want to wait a reshuffle before you go for the potion and the golem, but then you run the risk of overpaying for both of them. Draw 6p? Do you want the gold or the golem?
Familiar - I'm sure that Geronimo0 has simmed it, but I'm pretty sure that opening potion + $2 terminal/silver is the way to go here, but if you fail to buy the familiar on turn 3/4, then bad things happen. Do you want to have some real rage? You are 2nd player, your potion falls to turn 5 AND you draw 2p, and your opponent has already bought 2 familiars.
Alchemist - Not as bad as familiar - although just as hard to buy. Since they are more of a long term play - its not as crippling to fail to buy them early. Still not great though.
Forge - The ability to buy buy forge on turn 3 is obscenity.
King's Court - This will show up again - but as others have pointed out, getting 7 to buy KC is hard - but the value in pulling it off is crazy.
Goons - First one to goons has a decent advantage.
$5 Cards - There are several cards that are significantly more valuable if you can buy them early. Sometimes you get lucky and can buy them on turn 1! Trading Post, Mountebank, Witch, Torturer....
Mint - Did you happen to draw 5+ coppers? Sweet! Did you have silver + 3 coppers instead? Sorry - you lose. This is low on my list because it is rarely pivotal. There is a special case of Mint / Fools Gold + 5/2 split, but we'll save fool's gold for later.
2. Luck in ability to use the card to its fullest effect due to combinations
Tournament - I think this is self explanatory. First you had to buy an early province. Then you have to line it up with yours. If you go heavy on tournaments, you can get lucky and prize sweep. If you go heavy on tournaments and your opponent blocks it - you're f'd. Unlike other lucky cards (treasure map is going to get its time) - ignoring tournament is generally a bad idea.
Remake - Lets look at two players. They both open Remake / Silver. On turn 3, player 1 draws Remake, 2 estates and 1 copper, and 1 silver. He remakes his 2 estates into silvers, buys another silver, and draws his next hand: 5 coppers. Player 2 draws Remake + 4 Coppers. He trashes 2 coppers, and ends his turn. He draws his next Hand - Estate x3, Copper x2. Turn 4 - Player 1 Buys a Wharf. Want to guess how this game is end?
Baron Same as above. One person uses baron to buy an early game forge. The other person draws it with 4 coppers.
Steward - see above.
Salvager - see above.
Chapel - see above. The difference between "Ultimate Chapel" (Trash 3 estates and 1 copper, buy a Gold on Turn 4) and "Nightmare Chapel" - Trash 4 coppers, do nothing.
Young Witch - Best case - you draw the YW with your silver, buy a nice $5 card, and your opponent takes a curse. Worse case - your YW doesn't get you to 5, your opponent blocks you with the bane.
Treasure Map - A turn 5 treasure map hit is obscene. Turn 10? Not so much. This doesn't bother me much - because on average buying tmap is a bad idea.
King's Court - Did you draw your KC with an action? Awesome sauce. A cursing action? Good game sir. Another king's court and a card drawer? WOOOOOOOHOOOOO. Did you draw it with treasures and estates? Not so much. Added bonus rage if you have multiple KC's, and you draw them dead together.
Throne Room - As above, but less exciting
$Village - Did you draw it with 2 actions? Cool. Did you draw all your villages in one hand, and your actions in another? Boo.
Counting House Did you draw it after a reshuffle?
Chancellor Did you use it to buy a gold on T3 and reshuffle it? AWESOME. Did it show up on T3 with 3 estates?
3. Cards where the effect of playing them results in randomness.
Swindler - I swindle your estate into an estate. You swindle my chapel into an estate. I swindle your province into a province. You swindle my duchy into a counting house.
Jester - I cloned your king's court. You hit my silver.
Finally - some bad cards that are random, but generally bad so its hard to have rage.
Saboteur
Tribute
Thief
Pirate Ship
Probably some more here, but I've posted enough for today.