If you want to check the traffic, number of visitors of your own site, you can install Google Analytics, which is free and can track the daily, weekly, and monthly page views and unique visits your site receives. The information tends to be most precise and is only available to you.
If you want more than just basic data but all aspects of online experience to optimize your site, you can try Webtrends.com. However, it is not free to use.
If you are not the owner of a site, but like to check the traffic a site gets, you can use Alexa, Trafficestimate, or StatCounter.