The separation of code into layers brings benefits beyond just C# language.
If your data access code is kept in a separate layer, it will be easy to adjust it to work with a different database. Database-specific code will be encapsulated in this layer while clients will work with database-agnostic interfaces. Therefore changes here will not affect the business layer implementation.
If your business logic is kept in one place, you will be able to offer its services to other applications, for example, to serve requests made via web services.
If your code is clean and well structured, the maintenance efforts will be kept lower. Whenever you need to change something, you'll know where to find the responsible code, what to change and how to assure the change will not affect the rest of the code.
As for ASP.NET, not following the separation of concerns has caused many projects to turn into a giant code blurb - presentation code performs business decisions, code-behind talks directly to the database whenever no suitable business method exists, database gets written to from many places, dataflow is following multiple paths which are difficult to trace, changes in one path not introduced to all of them will break integrity and cause data corruption => Result? Almost unmaintainable code black box where any change requires more and more effort until it stalls - project is "finished". Technical bankruptcy.