There are many advantages of Stored Procedures.
I have to pick only ONE. It is tough question.
I answered : Execution Plan Retention and Reuse

(SP are compiled and their execution plan is cached and used again to when the same SP is executed again)
Not to mentioned I received the second question following my answer : Why? Because all the other advantage known (they are mentioned below) of SP can be achieved without using SP. Though Execution Plan Retention and Reuse can only be achieved using Stored Procedure only.

• Execution plan retention and reuse
• Query auto-parameterization
• Encapsulation of business rules and policies
• Application modularization
• Sharing of application logic between applications
• Access to database objects that is both secure and uniform
• Consistent, safe data modification
• Network bandwidth conservation
• Support for automatic execution at system start-up
• Enhanced hardware and software capabilities
• Improved security
• Reduced development cost and increased reliability
• Centralized security, administration, and maintenance for common routines

Reference : Pinal Dave (http://www.SQLAuthority.com)