What happens to a declared, uninitialized variable in C? Does it have a value?

Static variables (file scope and function static) are initialized to zero:

int x; // zero
int y = 0; // also zero

void foo() {
    static int x; // also zero
}

Non-static variables (local variables) are indeterminate. Reading them prior to assigning a value results in undefined behavior.

void foo() {
    int x;
    printf("%d", x); // the compiler is free to crash here
}

In practice, they tend to just have some nonsensical value in there initially - some compilers may even put in specific, fixed values to make it obvious when looking in a debugger - but strictly speaking, the compiler is free to do anything from crashing to summoning demons through your nasal passages.

As for why it's undefined behavior instead of simply "undefined/arbitrary value", there are a number of CPU architectures that have additional flag bits in their representation for various types. A modern example would be the Itanium, which has a "Not a Thing" bit in its registers; of course, the C standard drafters were considering some older architectures.

Attempting to work with a value with these flag bits set can result in a CPU exception in an operation that really shouldn't fail (eg, integer addition, or assigning to another variable). And if you go and leave a variable uninitialized, the compiler might pick up some random garbage with these flag bits set - meaning touching that uninitialized variable may be deadly.

0 if static or global, indeterminate if storage class is auto

C has always been very specific about the initial values of objects. If global or static, they will be zeroed. If auto, the value is indeterminate.

This was the case in pre-C89 compilers and was so specified by K&R and in DMR's original C report.

This was the case in C89, see section 6.5.7 Initialization.

If an object that has automatic storage duration is not initialized explicitely, its value is indeterminate. If an object that has static storage duration is not initialized explicitely, it is initialized implicitely as if every member that has arithmetic type were assigned 0 and every member that has pointer type were assigned a null pointer constant.

This was the case in C99, see section 6.7.8 Initialization.

If an object that has automatic storage duration is not initialized explicitly, its value is indeterminate. If an object that has static storage duration is not initialized explicitly, then:
— if it has pointer type, it is initialized to a null pointer;
— if it has arithmetic type, it is initialized to (positive or unsigned) zero;
— if it is an aggregate, every member is initialized (recursively) according to these rules;
— if it is a union, the first named member is initialized (recursively) according to these rules.

As to what exactly indeterminate means, I'm not sure for C89, C99 says:

3.17.2
indeterminate value
either an unspecified value or a trap representation

But regardless of what standards say, in real life, each stack page actually does start off as zero, but when your program looks at any auto storage class values, it sees whatever was left behind by your own program when it last used those stack addresses. If you allocate a lot of auto arrays you will see them eventually start neatly with zeroes.

You might wonder, why is it this way? A different SO answer deals with that question, see: https://stackoverflow.com/a/2091505/140740