I have a controller that currently does not specify 'with sharing'. I would like to be able to add these keywords but I don't want it to break on existing users. It's basically an aggregate report. One of the queries, queries for the number of Case the User created (Not current owner). Will they still have access to these cases that they created even if they are no longer the owner? (They do NOT have view all permissions.)
It depends on your sharing rules. Can they see the record in the UI? If so, then you should be good. In general, just because you created a record doesn't mean you'll still have access to it after the owner changes. Ownership is the king of sharing and determines most sharing unless you also have criteria based sharing rules in place as well.