How to make an autocomplete address field with google maps api?

Like others have mentioned, the Google Places Autocomplete API is missing some important functions. Case in point, Google will not validate that the street number is real, and they also will not put it into a standardized format. So, it is the user's responsibility to enter that portion of the address correctly.

Google also won't predict PO Boxes or apartment numbers. So, if you are using their API for shipping, address cleansing or data governance, you may want one that will validate the building number, autocomplete the unit number and standardize the information.

Full Disclosure, I work for SmartyStreets

It is easy, but the Google API examples give you detailed explanation with how you can get the map to display the entered location. For only autocomplete feature, you can do something like this.

First, enable Google Places API Web Service. Get the API key. You will have to use it in the script tag in html file.

<input type="text" id="location">
<script type="text/javascript" src="https://maps.googleapis.com/maps/api/js?key=[YOUR_KEY_HERE]&libraries=places"></script>
<script src="javascripts/scripts.js"></scripts>

Use script file to load the autocomplete class. Your scripts.js file will look something like this.

    // scripts.js custom js file
$(document).ready(function () {
   google.maps.event.addDomListener(window, 'load', initialize);
});

function initialize() {
    var input = document.getElementById('location');
    var autocomplete = new google.maps.places.Autocomplete(input);
}

Below I split all the details of formatted address like City, State, Country and Zip code. 
So when you start typing your street name and select any option then street name write over street field, city name write over city field and all other fields like state, country and zip code will fill automatically. 
Using Google APIs.
------------------------------------------------
<script type="text/javascript"
src="http://maps.googleapis.com/maps/api/js?sensor=false&libraries=places"></script>
<script type="text/javascript">
google.maps.event.addDomListener(window, 'load', function() {
    var places = new google.maps.places.Autocomplete(document
            .getElementById('txtPlaces'));
    google.maps.event.addListener(places, 'place_changed', function() {
        var place = places.getPlace();
        var address = place.formatted_address;
        var  value = address.split(",");
        count=value.length;
        country=value[count-1];
        state=value[count-2];
        city=value[count-3];
        var z=state.split(" ");
        document.getElementById("selCountry").text = country;
        var i =z.length;
        document.getElementById("pstate").value = z[1];
        if(i>2)
        document.getElementById("pzcode").value = z[2];
        document.getElementById("pCity").value = city;
        var latitude = place.geometry.location.lat();
        var longitude = place.geometry.location.lng();
        var mesg = address;
        document.getElementById("txtPlaces").value = mesg;
        var lati = latitude;
        document.getElementById("plati").value = lati;
        var longi = longitude;
        document.getElementById("plongi").value = longi;            
    });
});

Well, better late than never. Google maps API v3 now provides address autocompletion.

API docs are here: http://code.google.com/apis/maps/documentation/javascript/reference.html#Autocomplete

A good example is here: http://code.google.com/apis/maps/documentation/javascript/examples/places-autocomplete.html