I think it depends upon the context and field.
For instance, on program committees in my field, once you've submitted your own review, it is normal to know who the other reviewers are and be able to see their reviews. (As a program committee member, I've always been able to see other reviewers' reviews and see their identity. If I was barred from doing so, I would probably refuse to serve on the program committee.) I always read the other reviewers' reviews, and sometimes discover that I'd missed something important. It is not uncommon for me to adjust my review in light of insightful comments found in other reviews. Therefore, I think it is helpful to be able to read other reviews.
Generally, I think the reviewing process assumes that reviewers will be independent. This is important, to give authors a fair shake and combat groupthink. For instance, in my field, we generally try to ensure that every submitted paper receives at least 2 reviews (usually at least 3 reviews). Why do we do this? Because we know that reviewers are human and can make mistakes, and it is possible for one reviewer to dislike a paper that is nonetheless great and worthy of publication. Therefore, our system relies upon reviewers to independently evaluate the paper in their initial review, without talking to other reviewers. If all reviewers got together and shared notes before forming their own evaluation or submitting their own review, it would create significant dangers of groupthink and undermine the purpose of having multiple reviewers read every paper.
On the other hand, once you and the other reviewer have submitted your initial review, it's probably fair game to exchange notes -- but this may be dependent upon the culture in your field or conference/journal. If you are not familiar with the culture, I recommend that you contact the program committee chair or journal editor to find out what process they want you to follow.