Entity Framework is just a ORM Framework to access data, for more have a look on below links:
http://en.wikipedia.org/wiki/Object-relational_mapping[
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http://en.wikipedia.org/wiki/List_of_object-relational_mapping_software[
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There are many applications developed in ASP.NET MVC without Entity Framework.
I have done CRUD opertaions without Entity framework here (I have used ASP.NET MVC 4 and XML files as data source):
CRUD Operations using Partial View and jQueryUI in ASP.NET MVC4 - Part 1[
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Other than that you can use ADO.NET, LINQ to SQL, Sevices or any other mechanics to fulfill the need of persistence storage of your application. If you do not need any data storage, no need to use anything like that.
Hope this will help you. Thanks.