Is it possible to use an input value attribute as a CSS selector?

It is possible, if you're using a browser which supports the CSS :valid pseudo-class and the pattern validation attribute on inputs -- which includes most modern browsers except IE9.

For instance, to change the text of an input from black to green when the correct answer is entered:

input {
  color: black;
}
input:valid {
  color: green;
}

<p>Which country has fifty states?</p>

<input type="text" pattern="^United States$">

Yes, but note: since the attribute selector (of course) targets the element's attribute, not the DOM node's value property (elem.value), it will not update while the form field is being updated.

Otherwise (with some trickery) I think it could have been used to make a CSS-only substitute for the "placeholder" attribute/functionality. Maybe that's what the OP was after? :)

As mentioned before, you need more than a css selector because it doesn't access the stored value of the node, so javascript is definitely needed. Heres another possible solution:

<style>
input:not([value=""]){
border:2px solid red;
}
</style>

<input type="text" onkeyup="this.setAttribute('value', this.value);"/>

You can use Css3 attribute selector or attribute value selector.

/This will make all input whose value is defined to red/

input[value]{
color:red;
}

/This will make conditional selection depending on input value/

input[value="United States"]{
color:red;
} 

There are other attribute selector like attribute contains value selector,

input[value="United S"]{
color: red;
}

This will still make any input with United state as red text.

Than we attribute value starts with selector

input[value^='united']{
color: red;
}

Any input text starts with 'united' will have font color red

And the last one is attribute value ends with selector

input[value$='States']{
color:red;
}

Any input value ends with 'States' will have font color red

Sure, try:

input[value="United States"]{ color: red; }

jsFiddle example.

Refreshing attribute on events is a better approach than scanning value every tenth of a second...

http://jsfiddle.net/yqdcsqzz/3/

inputElement.onchange = function()
{
    this.setAttribute('value', this.value);
};

inputElement.onkeyup = function()
{
    this.setAttribute('value', this.value);
};

In Chrome 72 (2019-02-09) I've discovered that the :in-range attribute is applied to empty date inputs, for some reason!

So this works for me: (I added the :not([max]):not([min]) selectors to avoid breaking date inputs that do have a range applied to them:

input[type=date]:not([max]):not([min]):in-range {
    color: blue;
}

Screenshot:

Here's a runnable sample:

window.addEventListener( 'DOMContentLoaded', onLoad );

function onLoad() {
    
    document.getElementById( 'date4' ).value = "2019-02-09";
    
    document.getElementById( 'date5' ).value = null;
    
}

label {
    display: block;
    margin: 1em;
}

input[type=date]:not([max]):not([min]):in-range {
    color: blue;
}

<label>
    <input type="date" id="date1" />
    Without HTML value=""
</label>
    
<label>
    <input type="date" id="date2" value="2019-02-09" />
    With HTML value=""
</label>

<label>
    <input type="date" id="date3" />
    Without HTML value="" but modified by user
</label>
    
<label>
    <input type="date" id="date4" />
    Without HTML value="" but set by script
</label>
    
<label>
    <input type="date" id="date5" value="2019-02-09" />
    With HTML value="" but cleared by script
</label>

Following the currently top voted answer, I've found using a dataset / data attribute works well.

//Javascript

const input1 = document.querySelector("#input1");
input1.value = "0.00";
input1.dataset.value = input1.value;
//dataset.value will set "data-value" on the input1 HTML element
//and will be used by CSS targetting the dataset attribute

document.querySelectorAll("input").forEach((input) => {
  input.addEventListener("input", function() {
    this.dataset.value = this.value;
    console.log(this);
  })
})

/*CSS*/

input[data-value="0.00"] {
  color: red;
}

<!--HTML-->

<div>
  <p>Input1 is programmatically set by JavaScript:</p>
  <label for="input1">Input 1:</label>
  <input id="input1" value="undefined" data-value="undefined">
</div>
<br>
<div>
  <p>Try typing 0.00 inside input2:</p>
  <label for="input2">Input 2:</label>
  <input id="input2" value="undefined" data-value="undefined">
</div>