Know all possible arrangements of 32 pieces on 64 squares. Impossible you say? Maybe. So the most possible thing would be to be aware of how all the different types of pieces inter-function / counter-function with/ against one another.
How many Pattern Recognitions?
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Jun 27, 2013
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It depends on the strict definition, but if you define a pattern as a typical arrangement of pieces + a typical move/manoeuvre associated with the set-up, we're talking about thousands of patterns.
But probably knowing 200-300 of those patterns is enough to be a very decent player (~1800 OTB).
According to some research, GMs would know ~100 000 patterns, though I don't know how they landed on this high figure 
Psychologist Adriaan de Groot did ground breaking research on how chess grandmasters think compared to amateurs, and I seem to recall he thought grandmasters knew a few tens of thousands patterns.
There are of course many many different skewers, and a lot more ways of forcing the opponent to go into a skewer on the next few moves.
If I have to guess from how many puzzles and so on I've done in the past (books, tactics trainer, chesstempo etc) and from how often I recognize the general situation, I'd say that I as a 2000-ish player have a few thousand of them memorized.
Besides tactics, there are of course many positional and strategical patterns too, and I'm not nearly as good at them -- to learn those I can't just do puzzles on websites, I'd have to work...
Also, trainers like Dvoretsky argue that getting good at chess is not merely a matter of learning patterns; you need to have a good verbal understanding of chess positions as well (given some random position, explain in words what's going on). So you can figure out the inevitable positions that are not some pattern you've seen before.
Groot estimated 10,000 for masters and as many as 100,000 for grandmasters.
Also he said masters calculate more deeply while grandmasters calculate less but the moves they look at are more relevant.
Also as hicetnunc said, a simple pattern like a fork doesn't count. More like a given pawn structure with pieces in such a way relates to typical plans and maneuvers. The maneuvers may be tactical or a mating attack.
Having never seen this addressed, I'll venture a dangerously dumb question:
Realizing there may be several variations to each, and always hearing people talk about " pattern recognition " Would anyone care to venture a guess on How many basic pattern recognitions are there?? 50? 100? From another viewpoint, once you know 25 patterns, do you still have a long way to go? Would anyone care to elaborate?
Just starting the list,
1) pawn forks
2) knight forks
3) bishop/rook/Queen pins
4) Greek/Greco mates
5) Various Skewers
etc.
What's a rough idea on how many pattern recog's to get to a 1800 level? 2000 level? 2200?