There is some built-in binary search code but not in the core language as far as I know.
There is
BinarySearch
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 forma compiled form of Leonid's code from: