Maximum Concatenated Product
CJam, 32 28 23 12 bytes

0le!f{~*}:e&gt;


Try it online in the CJam interpreter.

Thanks to @user23013 for helping me save 16 whole bytes!

Idea

Permuting the characters in the input string divides it into integers (groups of consecutive digits) separated by spaces. By pushing a zero and then evaluating the permuted input string, we push two or more integers. Multiplying the topmost two will result either in the product of the input divided into exactly two integers or some suboptimal value.

Code

 le!         e# Push all possible character permutations of the input.
0   f{  }    e# For each permutation:
             e#   Push 0, then the permuted string.
      ~      e#   Evaluate the string. Pushes one or more integers.
       *     e#   Multiply the two topmost integers.
         :e&gt; e# Retrieve the greatest integer in the array.