Count nodes that referenced current node in VIews
In the Advanced section of the view's configuration, there is a subsection Other. This subsection holds an item Use aggregation. Turn this item on. This allows you to configure the Aggregation settings for each field in the Fields section. One option is to use COUNT.

What remains is to navigate from the current node to the nodes that reference the current node. In Drupal 6, this could be done with the Reverse Node Reference module, which suggests the References module for Drupal 7. I think you have to add a Relationship then add a Node:Nid field that uses this relationship and is aggregated using COUNT.