The limit is across both Standard and Custom Objects as 300 Maximum rules with 50 Criteria Based rules on Enterprise and Unlimited/Performance Editions only.
Criteria based rules are allowed on some standard objects as well as custom objects
You can create criteria-based sharing rules for accounts, opportunities, cases, contacts, leads, campaigns, and custom objects. You can create up to 50 criteria-based sharing rules per object.
On an object where the OWD setting is 'Controlled by Parent' you will not be able to set up sharing rules, so you need to change this, e.g on Contact to either 'Private', 'Public Read only' or 'Public Read/Write' to add sharing rules on this specific object.