The static using declaration allows invoking static methods without the class
name.
In C# 5
using System;
Console.WriteLine("Hello, World!");
In C# 6
using static System.Console;
WriteLine("Hello, World");

With expression-bodied methods, a method that includes just one statement can
be written with the lambda syntax.
In C# 5
public bool IsSquare(Rectangle rect)
{
return rect.Height == rect.Width;
}
In C# 6
public bool IsSquare(Rectangle rect) => rect.Height == rect.Width;

Similar to expression-bodied methods, one-line properties with only a get accessor
can be written with the lambda syntax
In C# 5
public string FullName
{
get
{
return FirstName +"" + LastName;
}
}
In C# 6
public string FullName => FirstName +"" + LastName;

In C# 5
public class Person
{
public Person()
{
Age = 24;
}
public int Age {get; set;}
}
In C# 6
public class Person
{
public int Age {get; set;} = 42;
}

To implement read-only properties, C# 5 requires the full property syntax. With
C# 6, you can do this using auto-implemented properties.
In C# 5
private readonly int _bookId;
public BookId
{
get
{
return _bookId;
}
}
In C# 6
public BookId {get;}

With the new nameof operator, names of fields, properties, methods, or types can
be accessed. With this, name changes are not missed with refactoring.

In C# 5
public void Method(object o)
{
if (o == null) throw new ArgumentNullException("o");
In C# 6
public void Method(object o)
{
if (o == null) throw new ArgumentNullException(nameof(o));

The null propagation operator simplifies null checks.
In C# 5
int? age = p == null ? null : p.Age;
var handler = Event;
if (handler != null)
{
handler(source, e);
}
In C# 6
int? age = p?.Age;
handler?.Invoke(source, e);

The string interpolation removes calls to string.Format. Instead of using
numbered format placeholders in the string, the placeholders can include
expressions.
In C# 5
public override ToString()
{
return string.Format("{0}, {1}", Title, Publisher);
}
In C# 6
public override ToString() => $"{Title} {Publisher}";

Dictionaries can now be initialized with a dictionary initializer—similar to the
collection initializer.
In C# 5
var dict = new Dictionary<int, string>();
dict.Add(3,"three");
dict.Add(7,"seven");
In C# 6
var dict = new Dictionary<int, string>()
{
[3] ="three",
[7] ="seven"
};

In C# 5
try
{
//etc.
} catch (MyException ex)
{
if (ex.ErrorCode != 405) throw;
// etc.
}
In C# 6
try
{
//etc.
} catch (MyException ex) when (ex.ErrorCode == 405)
{
// etc.
}

await can now be used in the catch clause. C# 5 required a workaround.
In C# 5
bool hasError = false;
string errorMessage = null;
try
{
//etc.
} catch (MyException ex)
{
hasError = true;
errorMessage = ex.Message;
} 
if (hasError)
{
await new MessageDialog().ShowAsync(errorMessage);
}
In C# 6
try
{
//etc.
} catch (MyException ex)
{
await new MessageDialog().ShowAsync(ex.Message);
}