You can verify that a bot accessing your server really is Googlebot (or another Google user-agent) by using a reverse DNS lookup, verifying that the name is in the googlebot.com domain, and then doing a forward DNS lookup using that googlebot name. This is useful if you're concerned that spammers or other troublemakers are accessing your site while claiming to be Googlebot.
> host 220.127.116.11
18.104.22.168.in-addr.arpa domain name pointer
> host crawl-66-249-66-1.googlebot.com
crawl-66-249-66-1.googlebot.com has address 22.214.171.124
Google doesn't post a public list of IP addresses for webmasters to whitelist. This is because these IP address ranges can change, causing problems for any webmasters who have hard coded them. The best way to identify accesses by Googlebot is to use the user-agent (Googlebot).