Check the $_SERVER['HTTP_USER_AGENT'] for some of the strings listed here:
http://www.useragentstring.com/pages/useragentstring.php
Or more specifically for crawlers:
http://www.useragentstring.com/pages/useragentstring.php?typ=Crawler
If you want to -say- log the number of visits of most common search engine crawlers, you could use
$interestingCrawlers = array( 'google', 'yahoo' );
$pattern = '/(' . implode('|', $interestingCrawlers) .')/';
$matches = array();
$numMatches = preg_match($pattern, strtolower($_SERVER['HTTP_USER_AGENT']), $matches, 'i');
if($numMatches > 0) // Found a match
{
// $matches[1] contains an array of all text matches to either 'google' or 'yahoo'
}