Are default-initialized variables automatically zero?

Question

If I don't assign a value to a variable when I declare it, does it default to zero or just whatever was previously in the memory?

e.g.

float x;

Answer 1

A declared variable can be Zero Initialized, Value Initialized or Default Initialized.

The C++03 Standard 8.5/5 aptly defines each:

To zero-initialize an object of type T means:

— if T is a scalar type (3.9), the object is set to the value of 0 (zero) converted to T;
— if T is a non-union class type, each nonstatic data member and each base-class subobject
is zero-initialized;
— if T is a union type, the object’s first named data member is zero-initialized;
— if T is an array type, each element is zero-initialized;
— if T is a reference type, no initialization is performed.

To default-initialize an object of type T means:
— if T is a non-POD class type (clause 9), the default constructor for T is called (and the initialization is ill-formed if T has no accessible default constructor);
— if T is an array type, each element is default-initialized;
— otherwise, the object is zero-initialized.

To value-initialize an object of type T means:
— if T is a class type (clause 9) with a user-declared constructor (12.1), then the default constructor for T is called (and the initialization is ill-formed if T has no accessible default constructor);
— if T is a non-union class type without a user-declared constructor, then every non-static data member and base-class component of T is value-initialized;
— if T is an array type, then each element is value-initialized;
— otherwise, the object is zero-initialized

For example:

#include<iostream>
using namespace std;

static int a; //Zero Initialized
int b; //Zero Initialized

int main()
{
    int i;  //Undefined Behavior, Might be Initialized to anything
    static int j; //Zero Initialized

    cout<<"\nLocal Uninitialized int variable [i]"<<i<<"\n";

    cout<<"\nLocal Uninitialized Static int variable [j]"<<j<<"\n";

    cout<<"\nGlobal Uninitialized Static int variable [a]"<<a<<"\n";

    cout<<"\nGlobal Uninitialized int variable [b]"<<b<<"\n";

    return 0;
}

You will notice The results for variable i will be different on different compilers. Such local uninitialized variables SHOULD NEVER be used. In fact, if you turn on strict compiler warnings, the compiler shall report an error about it. Here's how codepad reports it an error.

cc1plus: warnings being treated as errors
In function 'int main()':
Line 11: warning: 'i' is used uninitialized in this function

Edit: As rightfully pointed out by @Kirill V. Lyadvinsky in the comments, SHOULD NEVER is a rather very strong word, and there can be perfectly valid code which might use uninitialized variables as he points out an example in his comment. So, I should probably say:
You should never be using uninitialized variables unless you know exactly what you are doing.