How often should I use try and catch in C#?

When writing a C# application whose #1 priority is to never crash, how often should I used a try-catch block?

Can I encapsulate all the statements in a method in try-catch blocks?

public void SomeMethod()
{
    try
    {
        // entire contents of the function
        // library calls
        // function calls
        // variable initialization .. etc
    }
    catch (Exception e)
    {
        // recover
    }
}

What are the downsides to wrapping everything in try-catch blocks?