Here are my votes, noting my differences with theory in bold. Disclaimer: in 2p my strategy has been emphasize tech and icon dominance over scoring and achievements so I can win in whatever way I please in era 8-10. I'm not sure if this is really as good a strategy as I think it is; theory suggested otherwise in another thread. But as such I think the early cards that focus on the score pile are the least powerful—while my opponent is claiming achievements 1, 2, and 3, I'm splaying all my piles right and drawing Factories and Clocks.
Best: Mysticism. However, in my starting hand, I would rather have Domestication, Sailing, The Wheel, in that order. Domestication gets the edge because it gives you control over what you meld. But once I'm getting my third or fourth age 1 card, Mysticism is the best. Honorable mention to Agriculture, which becomes by far the most powerful 1 in later ages and can score a lot of points quickly.
Best: Mathematics. As long as you're careful not to fall too far behind in key icons and get obliterated, you can get way ahead with this guy. Return a 2, draw and meld a 3. Draw a 3. Return a 3, draw and meld a 4. Draw a 4. You'll be building factories while your opponent is still banging rocks together.
Worst: Currency. Scoring 2 or 4 points at the cost of 1 or 2 cards is not going to get you far. c.f. Agriculture.
Second worst: Canal Building: almost always useless when you're in age 2 but occasionally, if it's still showing in a later age, it randomly does something amazing for you (in either direction).
Third worst: Mapmaking: they may not have a 1 in their score pile, and even if they do, taking their 1 and then scoring a 1, for a net change of just three points, just doesn't seem worth a valuable action.
Best: Machinery. So overpowered. It profoundly limits your opponent's second action: they simply can't end their turn with a high card, or several small cards, in their hand, or you will turn the crank on them.
Feudalism. Medicine. As with Canal Building, this is too early for this effect. Trading a 1 or 2 in your score pile for a 3 or 4 in theirs is rarely worth an action, and you can usually only do it once or twice. Feudalism at least sets up a splay or two to cement your castle lead, and a good portion of the time it will also nab a free card out of their hand.
Best: Gunpowder can sometimes blow the game wide open, so I can agree with that pick. Second place is
Printing Press Experimentation—draw and meld a 5 is random, but it's going to be very good for you no matter what happens. Next I rank Reformation, which sometimes gives you a tremendous lead on icons. I put Printing Press 4th—it's just a little hard to set up. You really need a purple 4+ to make it worthwhile, or else this is a really bad Experimentation. And you have to have a card in your score pile that you're willing to part with. You might need those cards, or you may not have bothered to score a single card by this point. Anatomy can be even more devastating than Gunpowder—in a good number of the games I draw Anatomy, I am able to obliterate my opponent's board and score pile—but it isn't quite consistent enough—my opponent's score pile doesn't always line up with their top cards, or sometimes they Metalworking'd themselves plenty of chump blockers.
Worst: Colonialism's tuck dogma is too small to be worth an action, but its icons (Factory, Factory, Lightbulb) can be a quite valuable upgrade to your red pile once Castles have been eclipsed. So I actually think Perspective is the worst 4. You need four Lightbulbs in play and must spend three cards in your hand just to score two of them—ain't nobody got time for that! Agriculture would give you more points for less work. And the
purple yellow that you'd cover with Perspective was probably more useful than the red card that you'd cover with Colonialism.
Best: Chemistry can rapidly promote your score pile to all 6s, and it splays your blue cards right, and which often reveals valuable Lightbulbs. But Coal splays your red cards right, which often reveals valuable Factories, and tucks a 5, and has an optional ability to score two cards (also possibly exposing a 3rd-from-the-top card, possibly even one tucked by Coal). So I give Coal the edge over Chemistry. But it's very close. For a player who already has some points and achievements, either card's scoring potential can quickly put the game away.
Not the best:
Astronomy's ability seems powerful but it's hit-or-miss and sometimes randomly covers a card you wanted. Measurement probably has the highest potential for a single execution—splaying your giant pile right and drawing you a 7 or higher—but that situation presents itself less than half the time.
probably definitely. Splaying a color right is often great, but making them draw a card from their score pile might even help them. Societies is rarely useful—they usually don't have a non-purple top card with a lightbulb that's better than your top card of that color—and giving them a replacement draw of a 5 is quite a cost, but sometimes it can ruin them by giving you their best card (possibly the only 6 on the board).
Best: Industrialization. If you have a Factory lead and a score lead (or a way to grab the score lead), you can just tuck the entire 6-10 decks under your piles and snowball your way to victory. Being able to splay two different colors right really puts this card over the top. Even if you don't start with the Factory lead, if board conditions are right, it may only take the first activation for you to regain it. Even if you don't ride Industrialization through the 10s, you will have a lot of icons to work with. And if you're going for achievements, this will get you Monument. Second best is Vaccination, which can wreck a score pile, sometimes in just one or two activations, but the meld effects are random and might do more harm than good. Atomic Theory is solid but feels downright fair compared to Industrialization.
Worst: Encyclopedia. The highest cards in your score pile often won't be useful, and even if they are, it's usually not worth going backwards in score just to meld them. Metric System is the second worst. All it does is splay a pile right, which makes it much worse than other 6's that splay right and do something else. On the plus side, splaying any color right is versatile: it may let you get a key icon at a key moment and it can easily get you to the Wonder achievement.
Best: Lighting. Sometimes Bicycle will get you from 0 points to 30 or more in one fell swoop, but even in the best situations for Bicycle, Lightning will usually score you 14-21 while developing your icons, which seems like the stronger play to me most of the time. And in some cases, when your hand and your score pile are both a motley assortment of random cards, Bicycle may do very little.
Worst: Refrigeration. They return half rounded down, so they can always keep the one important card in their hand. And scoring one card from your hand at a time is too slow for Age 7 (c.f. Lightning and Bicycle). Railroad is awfully limited in use—you don't want to trade your hand for three 6's in age 7, but sometimes the 6 or even 7 pile is empty, and drawing some 7s and 8s is pretty good, and sometimes you do have a splay-right that's worth turning to a splay-up.
Best: Mobility. I agree with popsofctown—it is exceedingly rare that removing your opponent's two highest (non-red) top cards does not mess with their plans, and you also are nabbing those ~13 points per activation! Often you will want to activate this effect multiple times, either to win on points or achievements, remove an opponent's top card with a threatening ability, or just to stay ahead on icons.
I put Skyscrapers at second. It can often be a wrecking ball, absolutely devastating your opponent's board and advancing yours. Unless the one card you score them hands them the game, it will be hard for them to win after a successful Skyscrapers activation.
Next I put Mass Media—you can often decimate your opponent's score pile with just one activation, meanwhile splaying purple up.
Not the best:
Quantum Theory jumps you to 10, which is nice, but it requires two cards in hand and doesn't have any immediate impact on your icons or your opponent, which means it is sometimes too slow.
Rocketry: there will be times where it is one of the few cards that will stop your opponent from claiming the last achievement they need, and three clocks are nice, but there will be times that this card doesn't affect the board and so doesn't keep your opponent from winning some other way. And if this is your only source of clocks, it only removes one card per activation, which may even be too slow to counter your opponent's scoring engine.
Empiricism: hit-or-miss. It's occasionally a victory condition, and if you get lucky it can hugely develop your board in both top card age and splay.
Socialism. Antibiotics is even worse. The only thing this 8 does is turn up to three other cards in your hand (possibly 8's) into more, different, better 8's. c.f. Quantum Theory, which converts two cards in your hand to a 10 in your hand and a 10 in your score pile, almost always a better position for you.
Best: Satellites barely gets the edge over Computers. Sure, the 8 won't be as powerful as the 10, but choosing from three 8's gives you a much higher chance of doing something that actually helps you. The 8's are plenty strong—see above. Meanwhile activating a random 10 might just lose you the game.
Worst: Fission is pretty lose-lose—they will get to meld a card before you after the apocalypse. And Services is only a so-so score-pile-attacker, and actually un-develops your board. But actually, I have never seen anyone even try to use Collaboration: drawing and melding a single card is not a very powerful effect for a 9—c.f. Sailing!—even when you get to choose from two 9's, and adding a free 9 to your opponent's board is quite a cost for this privilege. (You can dream of covering their best card with some "bad" 9 while nabbing a "good" 9 for yourself, but this is extremely unlikely.)
It seems like you have to evaluate the 10s separately, based on whether you are meld-and-executing them involuntarily or not. :-) I went ahead and ranked them from best to worst:
1. Software: Want to run the 10 pile ASAP? Look no further! This card does it all—it improves your score and your board, and then does something crazy. Sure, it might make you randomly lose, but it makes it much more likely that you're going to win.
2. The Internet: Software without the auto-executing, making it slower but safer. Splaying green up may not benefit you before the game ends, but it might let you claim a special achievement or let you win by icons in some way.
3. Bioengineering: I find this is an easy way to win if I have icon/splay superiority. And scoring one of their top cards is a pretty strong effect even if you don't win the game.
4. Globalization: The first two parts of this card are almost identical to Bioengineering, but obviously the victory condition is reversed and tangential. Another reasonably quick way to win.
5. Robotics: A much worse Software. Instead of scoring a free 10 and developing your board, you score your top green card. Still, you may get lucky with the draw-and-execute-without-sharing.
6. Self Service: A nice victory condition that can never backfire (unlike other 10s that can let any player win the game, this one can only let the dogma-executor win). The fact that you don't have to share the dogma that you choose to execute can be a powerful loophole if you are behind on icons.
7. Stem Cells: It doesn't say "win the game," and it does require that you still have a considerable hand (so if you got here via Satellites, you may be out of luck), but this single card can turn around a game fast, getting you points to claim the last achievements or just win when the 10s run out. However, most of the time, you'd rather just score a fresh 10 and develop your board, or attack your opponent's board and score a card, like the first four 10's in my list do.
8. Databases: This is a big effect, but in most late-game scoring situations, it's just not big enough, especially since they get to pick which half of their score pile gets returned. Consider that, while you're doing Databases, your opponent is likely 1) scoring a 10 or multiple cards per action, or even worse, 2) winning the game on the dogma of some 9 or 10.
9. A.I. All it does is score you 10 points, which may or may not help you win the game, and then there's a small chance that it actually loses you the game instead. c.f. Software and The Internet, which also score you a ten and actually improve your board (and don't lose you the game). And if you're trying to win with A.I. deliberately, because you're more than 10 points behind, well it probably won't work because Software or Robotics will probably be stuck in a score pile or hand or in the deck.
10. Miniaturization: This can never affect the board or score piles in any way. It requires a second 10 in your hand, and all it does is draw you more 10s. As with Socialism in age 8, wouldn't you rather have just drawn one of those other, better 10s in the first place?
Edit: Perspective is yellow, not purple. Thanks eyhung.
Edit: Fleshed a few entries out a bit.