There are 1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976 (Quattuordecillion) +- possible key pairs.
How it works
Method 1
STEP 1:
You cover all eight planets in our solar system with storage devices which can store yottabytes of data.
STEP 2:
You find another eight planets in other solar systems and cover them with billions of supercomputers
STEP 3:
You generate every bitcoin key pair then store each of them in the storage devices, on the surface of those planets.
STEP 4:
You use the supercomputers and loop through the data
STEP 5:
Collect your reward
Estimated time of complition for one key: 256^256* years
Method 2
STEP 1:
Visit http://directory.io
STEP 2:
Flick through each page until you find your key pair
STEP 3:
Collect your reward
Estimated time of complition for one key: Dude I can't even tell you that. Maybe you should try it?