A var cannot be set to null since it needs to be statically typed.
var foo = null;
// compiler goes: "Huh, what's that type of foo?"
However, you can use this construct to work around the issue:
var foo = (string)null;
// compiler goes: "Ah, it's a string. Nice."
I don't know for sure, but from what I heard you can also use dynamic instead of var. This does not require static typing.
dynamic foo = null;
foo = "hi";
Also, since it was not clear to me from the question if you meant the varkeyword or variables in general: Only references (to classes) and nullable types can be set to null. For instance, you can do this:
string s = null; // reference
SomeClass c = null; // reference
int? i = null; // nullable
you can't initialise var with null, var needs to be initialised as a type otherwise it cannot be inferred, if you think you need to do this maybe you can post the code it is probable that there is another way to do what you are attempting.
C# is a strictly/strongly typed language. var was introduced for compile-time type-binding for anonymous types yet you can use var for primitive and custom types that are already known at design time. At runtime there's nothing like var, it is replaced by an actual type that is either a reference type or value type.
When you say,
var x = null;
the compiler cannot resolve this because there's no type bound to null. You can make it like this.
string y = null;
var x = y;
This will work because now x can know its type at compile time that is string in this case.
Well, as others have stated, ambiguity in type is the issue. So the answer is no, C# doesn't let that happen because it's a strongly typed language, and it deals only with compile time known types. The compiler could have been designed to infer it as of type object, but the designers chose to avoid the extra complexity (in C# null has no type).
One alternative is
var foo = new { }; //anonymous type
Again note that you're initializing to a compile time known type, and at the end its not null, but anonymous object. It's only a few lines shorter than new object(). You can only reassign the anonymous type to foo in this one case, which may or may not be desirable.
Initializing to null with type not being known is out of question.
Unless you're using dynamic.
dynamic foo = null;
//or
var foo = (dynamic)null; //overkill
Of course it is pretty useless, unless you want to reassign values to foo variable. You lose intellisense support as well in Visual Studio.
Lastly, as others have answered, you can have a specific type declared by casting;
var foo = (T)null;
So your options are:
//initializes to non-null; I like it; cant be reassigned a value of any type
var foo = new { };
//initializes to non-null; can be reassigned a value of any type
var foo = new object();
//initializes to null; dangerous and finds least use; can be reassigned a value of any type
dynamic foo = null;
var foo = (dynamic)null;
//initializes to null; more conventional; can be reassigned a value of any type
object foo = null;
//initializes to null; cannot be reassigned a value of any type
var foo = (T)null;