As a reviewer, how much raw data or code should you request?
If there are other reasons to reject the paper, then it's certainly unnecessary to request code/data.  If the paper looks like something that might be accepted, then you should ask yourself:


  Can I certify the correctness and significance of this work, to the necessary degree, with the information that is available?


Of course, the key is the phrase to the necessary degree.  To make things more concrete, you might consider:


  Would I feel comfortable if the whole world knew that I refereed and recommended acceptance of this paper?


If the answer is no, I don't have enough confidence in the results without seeing the raw data/code, then you should ask for it.  You're really doing the authors a favor here -- giving them the chance to convince you by providing additional evidence.

I would be very polite and make the request through the editor.  If the code and data are not forthcoming, you should probably say in your recommendation something like


  I find the results in this paper compelling if they are correct, but I cannot recommend it for publication without verifying the data/code that underlies those results.


Of course, the degree to which a referee is expected to verify the correctness of results varies greatly between fields.  But you can always choose a personal standard higher than what's usual in your field.  Just realize that good refereeing takes a significant time investment.