Well.. I´ve heard that something like 12.000 unique Magic cards have been created. And most of them exist in more than one copy...
Here are some questions we can discuss, argue, count, guess and troll about in this thread:
1. How many cards in all languages, including basic lands, exist in the world?
2. How many copies of rare/mythic cards exist? Roughly how many Black Lotuses, Restoration Angel, Dark Confidant etc exists?
3. Is it good or bad that Wizard keeps the total number of "sought-after cards" low? If certain cards are very attractive, would it be a better thing if Wizard printed more of them to make everyone happy?
4. How many boosters are released with every set?
Everything related to the total number of Magic cards, individual copies of certain cards, Wizards market strategy about this, funny mathematical stuff about how all Magic cards together would weight more than the moon and so on can be discussed in this thread.
It would be either an effort in futility... or simply an utter waste of time to try to account for a card count/total that encompasses total different numbers of printings (both based on set/reprints and foreign versions).
The most useful number is more a matter of what you hit in your first line, how many total unique Magic cards are there?
And there is definitely a potentially interesting discussion in breaking that down in terms of good/useful cards vs. chaff/filler... and also attempting to account for functional reprints.
4. You won't get this kind of info any more. There's info about card counts/print runs from earlier sets, but not recently.
The Black Lotus count is pretty easy to answer, since those print run numbers are available (and this comes up a couple times a month). I just took print run divided by cards per booster, and that answer divided by rares in the set (117 for B/U, 116 for A). I didn't take into account starter deck distribution.
Unlimited has roughly ~20,000 of any given rare
Beta has roughly ~4200 of any given rare
Alpha has roughly ~1500 of any given rare
Some of the early sets had print runs of 500 million cards, and it's hard to think that modern sets are print with less cards than those, so we could be talking about a million dark confidants in existence, or maybe more. Or maybe not, since it's still not hard to find some of the overprinted earlier sets.