According to the writers/director, that grey wolf symbolises Cloud's feelings of guilt over the deaths of Aerith and Zack. It makes sense, too - just look at where the symbol appears:

* The Buster Sword marking Zack's final resting place

* In the church, when Cloud finds Tifa and passes out before he can help her

* At the Forgotten City

* When he briefly meets Zack and Aerith in the Lifestream at the end, when he's almost killed. The wolf disappears at that point, as Cloud is beginning to forgive himself (that's my interpretation, anyway).