I found the same two solutions as did Charlie:
373   733
757   353
373   337

The condition  "[t]he cells of a 3 x 3 grid contain prime digits" implies that each digit that makes up the 3-digit prime must also be prime. Therefore the imposition made was by the poser's text of the problem. As the only digits that are prime are 2, 3, 5 and 7, the limit of digits is four. 

Given the note following the posed problem, "[t]here are at least two other arrangements where a non-prime digit may be used, and digit totals are not always prime" offers a separate problem. If permitted the multiple occurance of the non-prime digit, there are several solutions available:
113   373   313   313   313   733
151   751   751   151   757   383
311   313   313   313   313   337

Edited on December 1, 2008, 9:41 pm

Posted by Dej Mar on 2008-12-01 21:32:35