Ideal approach? - Shared Classes or Non Shared (Object based)

Whats the ideal approach while developing an  ASP .Net application.
1. Using normal classes and then using their functions by making objects? 
2. Using Shared (Static for C#) classes and their shared functions and accessing them without creating the objects.


My questions are
What are benefits and drawbacks of above both?
Can we face issues in simultaneous access of functions in 2nd case?
Will there be separate copies of functions and variables in memory for 2nd case or just a single copy?
What if our SqlConnection, SqlCommand and SqlAdapter are also shared? 
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