When should we use Radix sort?

Radix sort is harder to generalize than most other sorting algorithms. It requires fixed size keys, and some standard way of breaking the keys into pieces. Thus it never finds its way into libraries.

Edited according to your comments:

• Radix sort only applies to integers, fixed size strings, floating points and to "less than", "greater than" or "lexicographic order" comparison predicates, whereas comparison sorts can accommodate different orders.
• k can be greater than log N.
• Quick sort can be done in place, radix sort becomes less efficient.

The other answers here fail to give examples of when radix sort is actually used.

An example is when creating a "suffix array" using the skew DC3 algorithm (Kärkkäinen-Sanders-Burkhardt). The algorithm is only linear-time if the sorting algorithm is linear-time, and radix sort is necessary and useful here because the keys are short by construction (3-tuples of integers).