RJ (and others),
In the most general sense, a card's strength (expected value) is something like [the amount this helps you win the game] * [the amount of time it's useful] for each kingdom, or more accurately, the sum of its expected values across all possible kingdoms. I agree allfail is setting up a similar sort of calculation, but I don't think the factors he's using are meaningful. I'll get back to that.
Now, the [the amount of time it's useful] part, we can estimate by looking at a kingdom. KC, Expand, Monument, Laboratory, Remake, Hamlet, 4 other cards, no Colony. How often do you estimate you'll want KC in this kingdom? Maybe it's 10%, maybe it's 90%, maybe it's some other number. Let's call it 0.9. Now look at all the other possible kingdoms and do the same, then weigh these estimates together. My best estimate so far for KC seems to be ~0.68, WW's is ~0.55, chwhite's is ~0.85, etc. The best estimate if we look at the sum of all players on isotropic is ~0.84.
The [the amount this helps you win the game] is probably more difficult for us to properly estimate, but in theory we can compare our winrate when using a card to our winrate when not using a card, across all kingdoms. We have councilroom data for this too, but intuitively it seems to me that winrate estimates need a lot more time to converge than buy% estimates, and I would guess numbers from individuals probably are very uncertain here? Someone who's better at statistics than I am could probably calculate that, I'm sure. Whatever, it's mostly a thought experiment at this point.
I reject allfail's notion that these lists are subjective in nature. These things are quantifiable in principle, even if we might not be able to do the calculations properly/accurately. I hope I've given a better answer to what (I think) should go into a card strength evaluation now, at least.
The problem I have with a lot of the arguments brought up is that they're, at best, mere indicators of card strength, and at worst, not even that. KC isn't strong because it has a unique effect. KC might be strong AND have a unique effect, but a unique effect does not a good card make. Correlation does not imply causation; KC just happens to be both strong and unique (ish). Counter examples, cards that are bad and unique, have already been brought up (Saboteur, Counting House). KC is good because KC is good, not because of its uniqueness (seems I'm repeating myself from the old Cellar vs Warehouse thread now, heh).
Anyway as mentioned earlier, I guess one reason we disagree so much is because you look at this as a subjective list where you can more or less make things up because they're your opinion. I would suggest this works a lot better on a "favorite cards" list than a "best card" list. Taken to its extreme, I can claim Herbalist is the best card in Dominion because.. and then make something ridiculous up. It's all subjective anyway, right? I imagine people would respond with some reasonable things, and then suggest to me that maybe I just really like Herbalist?
Like, if you think "a card's ability to combo well with other cards" is a good critera to use for evaluating a card's strength, then that's fine and all that, but maybe you just really like building combo decks?
Anyway it's all good I hope, I can live with my imaginary objectiveness
Finally, as for the random numbers I threw out about game warping and stuff, you all very well might be right. I certainly didn't think very hard about it. Of course, in the more general sense, saying a card is game warping is really just a roundabout way of saying something like you probably need to buy it more often, and it'll probably be really good on average in those cases (as per the expected value calculations above); a card being "game warping" has no quantifiable meaning in itself. I think I might be thinking of "game warping" slightly differently, but then again maybe not, and I don't think it's a very important point.