How can I check the crawling history of our website?

Read your site logs

Check your web logs - see how many times googlebot has visited your site. You would typically get a regular visit from something looking like the following:

crawl-66-249-66-244.googlebot.com

Frequency depends on the site and how often Google detects you update it. In my experience most sites are visited at least once a day - highly active sites (such as CNN) much more frequently.

Or you can refer the traffic data through third-party tools.

by checking your site logs or you can used google webmaster tools that show crawling rate and history of a site!

use google s webmaster tools they are pretty informative

Thanks to all.. You give me a lot of information.....