Probability that either partnership will have enough to bid game, assuming a 26+ point game = 25.29% (1 in 3.95 deals)

Probability that either partnership will have enough to bid slam, assuming a 33+ point slam = .70% (1 in 143.5 deals)

Probability that either partnership will have enough to bid grandslam, assuming a 37+ point grandslam = .02% (about 1 in 5,848 deals)

Number of different hands a named player can receive = 635,013,559,600

Number of different hands a second player can receive = 8,122,425,444

Number of different hands the 3rd and 4th players can receive = 10,400,600

Number of possible deals = 52!/(13!)^4 = 53,644,737,765,488,792,839,237,440,000

Number of possible auctions with North as dealer, assuming that East and West pass throughout = 2^36 - 1 = 68,719,476,735

Number of possible auctions with North as dealer,
  assuming that East and West do not pass throughout =
128,745,650,347,030,683,120,231,926,111,609,371,363,122,697,557

Odds against each player having a complete suit = 2,235,197,406,895,366,368,301,559,999 to 1

Odds against receiving a hand with 37 HCP (4 Aces, 4 Kings, 4 Queens, and 1 Jack) = 158,753,389,899 to 1

Odds against receiving a perfect hand (13 cards in one suit) = 169,066,442 to 1
Odds against a Yarborough = 1827 to 1

Odds against both members of a partnership receiving a Yarborough = 546,000,000 to 1

Odds against a hand with no card higher than 10 = 274 to 1

Odds against a hand with no card higher than Jack = 52 to 1

Odds against a hand with no card higher than Queen = 11 to 1

Odds against a hand with no Aces = 2 to 1

Odds against being dealt four Aces = 378 to 1

Odds against being dealt four honors in one suit = 22 to 1

Odds against being dealt five honors in one suit = 500 to 1

Odds against being dealt at least one singleton = 2 to 1

Odds against having at least one void = 19 to 1

Odds that two partners will be dealt 26 named cards between them =  495,918,532,918,103 to 1

Odds that no players will be dealt a singleton or void = 4 to 1

Card Distribution (remaining two hands)
Hand Distribution (suits within a hand)
High Card Point Count (HCPs in one hand)
Miscellaneous Probabilities (assorted interesting odds)
Number of Cards (card quantity in a suit)
Posteriori Probability (example when additional information is known)
Suit Combinations (best lead and plays)
Expected Controls (based on HCP)

Also see books on Probabilities