Intenta usar $_POST en vez de $_REQUEST a ver como va:
<form id="contact" action="process.php"
method="post">
<fieldset>
<label for="name" id="name_label" style="font-size:16px;">Name</label>
<input type="text" name="name" id="name" size="50" value="" class="text-input" />
<label for="email" id="email_label" style="font-size:16px;">E-mail</label>
<input type="text" name="email" id="email" size="50" value="" class="text-input" />
<label for="subject" id="subject_label" style="font-size:16px;">Subject</label>
<input type="text" name="subject" id="subject" value="" class="text-input" />
<label for="msg" id="msg_label" style="font-size:16px;">Message</label>
<textarea cols="60" rows="10" name="msg" id="msg" class="text-input"></textarea>
<input type="submit" name="submit" class="button" id="submit_btn" value="Send Message" style="font-size:12px;"/><br />
<span class="error" id="name_error">Please enter name !</span>
<span class="error" id="email_error">Please enter email address !</span>
<span class="error" id="email_error2">Please enter valid email address !</span>
<span class="error" id="msg_error">Please enter message !</span>
</fieldset>
</form>
Codigo Php:
<?php
$emailTo = '
[email protected]';
$subject = $_
POST['subject'];
$name = $_
POST['name'];
$email = $_
POST['email'];
$msg = $_
POST['msg'];
$body = "Name: $name \n\nEmail: $email \n\nMessage: $msg";
$headers = 'From: '.$name.' <'.$email.'>' . "\r\n" . 'Reply-To: ' . $email;
mail($emailTo, $subject, $body, $headers);
?>