Actually, you can use a literal 0 anyplace you would use NULL.

Section 6.3.2.3p3 of the C standard states:

An integer constant expression with the value 0, or such an expression cast to type void *, is called a null pointer constant. If a null pointer constant is converted to a pointer type, the resulting pointer, called a null pointer, is guaranteed to compare unequal to a pointer to any object or function.

And section 7.19p3 states:

The macros are:

NULL

which expands to an implementation-defined null pointer constant

So 0 qualifies as a null pointer constant, as does (void *)0 and NULL. The use of NULL is preferred however as it makes it more evident to the reader that a null pointer is being used and not the integer value 0.

Note: This answer applies to the C language, not C++.

Null Pointers

The integer constant literal 0 has different meanings depending upon the context in which it's used. In all cases, it is still an integer constant with the value 0, it is just described in different ways.

If a pointer is being compared to the constant literal 0, then this is a check to see if the pointer is a null pointer. This 0 is then referred to as a null pointer constant. The C standard defines that 0 cast to the type void * is both a null pointer and a null pointer constant.

Additionally, to help readability, the macro NULL is provided in the header file stddef.h. Depending upon your compiler it might be possible to #undef NULL and redefine it to something wacky.

Therefore, here are some valid ways to check for a null pointer:

if (pointer == NULL)

NULL is defined to compare equal to a null pointer. It is implementation defined what the actual definition of NULL is, as long as it is a valid null pointer constant.

if (pointer == 0)

0 is another representation of the null pointer constant.

if (!pointer)

This if statement implicitly checks "is not 0", so we reverse that to mean "is 0".

The following are INVALID ways to check for a null pointer:

int mynull = 0;
<some code>
if (pointer == mynull)

To the compiler this is not a check for a null pointer, but an equality check on two variables. This might work if mynull never changes in the code and the compiler optimizations constant fold the 0 into the if statement, but this is not guaranteed and the compiler has to produce at least one diagnostic message (warning or error) according to the C Standard.

Note that the value of a null pointer in the C language does not matter on the underlying architecture. If the underlying architecture has a null pointer value defined as address 0xDEADBEEF, then it is up to the compiler to sort this mess out.

As such, even on this funny architecture, the following ways are still valid ways to check for a null pointer:

if (!pointer)
if (pointer == NULL)
if (pointer == 0)

The following are INVALID ways to check for a null pointer:

#define MYNULL (void *) 0xDEADBEEF
if (pointer == MYNULL)
if (pointer == 0xDEADBEEF)

as these are seen by a compiler as normal comparisons.

Null Characters

'\0' is defined to be a null character - that is a character with all bits set to zero. '\0' is (like all character literals) an integer constant, in this case with the value zero. So '\0' is completely equivalent to an unadorned 0 integer constant - the only difference is in the intent that it conveys to a human reader ("I'm using this as a null character.").

'\0' has nothing to do with pointers. However, you may see something similar to this code:

if (!*char_pointer)

checks if the char pointer is pointing at a null character.

if (*char_pointer)

checks if the char pointer is pointing at a non-null character.

Don't get these confused with null pointers. Just because the bit representation is the same, and this allows for some convenient cross over cases, they are not really the same thing.

References

See Question 5.3 of the comp.lang.c FAQ for more. See this pdf for the C standard. Check out sections 6.3.2.3 Pointers, paragraph 3.

In C and C++, pointers are inherently unsafe, that is, when you dereference a pointer, it is your own responsibility to make sure it points somewhere valid; this is part of what "manual memory management" is about (as opposed to the automatic memory management schemes implemented in languages like Java, PHP, or the .NET runtime, which won't allow you to create invalid references without considerable effort).

A common solution that catches many errors is to set all pointers that don't point to anything as NULL (or, in correct C++, 0), and checking for that before accessing the pointer. Specifically, it is common practice to initialize all pointers to NULL (unless you already have something to point them at when you declare them), and set them to NULL when you delete or free() them (unless they go out of scope immediately after that). Example (in C, but also valid C++):

void fill_foo(int* foo) {
    *foo = 23; // this will crash and burn if foo is NULL
}

A better version:

void fill_foo(int* foo) {
    if (!foo) { // this is the NULL check
        printf("This is wrong\n");
        return;
    }
    *foo = 23;
}

Without the null check, passing a NULL pointer into this function will cause a segfault, and there is nothing you can do - the OS will simply kill your process and maybe core-dump or pop up a crash report dialog. With the null check in place, you can perform proper error handling and recover gracefully - correct the problem yourself, abort the current operation, write a log entry, notify the user, whatever is appropriate.

In C, NULL is a macro that expands either to 0 or (void*)0 (or something that has a similar effect).

In the first case, you can not differentiate between NULL and 0, because they are literally the same.
In the second case, your code will cause a compile error, because you can't compare an integer variable with a pointer.