How many instances of 3-SAT are satisfiable? Consider the 3-SAT problem on n variables.  The number of possible distinct clauses is: 

$$C = 2n \times 2(n-1) \times 2(n -2) / 3! = 4 n(n-1)(n-2)/3 \text.$$

The number of problem instances is the number of all subsets of the set of possible clauses: $I = 2^C$.  Trivially, for each $n \ge 3$, there exist at least one satisfiable instance and one unsatisfiable instance.
Is it possible to calculate, or at least estimate, the number of satisfiable instance for any given n?
A long history of work on phase transitions in SAT has shown that for any fixed $n$, there's a threshold parametrized by the ratio of number of clauses to $n$ that decides satisfiability. Roughly speaking, if the ratio is less than 4.2, then with overwhelming probability the instance is satisfiable (and so a huge fraction of the number of instances with these many clauses and variables are satisfiable). If the ratio is slightly above 4.2, then the reverse holds - an overwhelming fraction of instances are unsatisfiable. 

The references are way too many to cite here: one source of information is the book by Mezard and Montanari. If anyone has sources for surveys etc on this topic, they could post it in comments or edit this answer (I'll make it CW)

References:
 - Achlioptas survey
 - Where the really hard problems are
 - Refining the phase transition in combinatorial search