There is some built-in binary search code but not in the core language as far as I know.

- There is [`BinarySearch`][1] from the *Combinatorica* package, which is still the function I use most often despite the fact that that package is now deprecated and loading it causes shadowing of some Symbols.

- There is the undocumented ``GeometricFunctions`BinarySearch`` but this function does not appear to perform particularly well.

When I need greater performance I typically use [a compiled form][2] of Leonid's code from: 

- https://mathematica.stackexchange.com/questions/2369/finding-all-elements-within-a-certain-range-in-a-sorted-list/2371#2371
 


  [1]: http://reference.wolfram.com/language/Combinatorica/ref/BinarySearch.html
  [2]: https://mathematica.stackexchange.com/a/30122/121