Assuming that you are running a blog that you are trying to get well known and potentially make money off of, chances are that you are going to want to be checking out your statistics to see how you are doing. There are a lot of statistics out there that you can follow and you can spend a lot of time looking into them.
That said, here is what I do when it comes to stats. Depending on how much work you are putting into your blog, you may want to do more or less. I personally check mine once a month and I track them in a spreadsheet so I can see how I am doing.
Google Analytics – I have my blogs set up on Analytics so when the month ends, I will go to their site and check out the numbers there. There is a lot of information there so it is important to determine what is important to know. I like to know how many unique visits I have, how many are new, and where the traffic is coming from.
Alexa – There are many sites that use your ranking in Alexa to determine if they want to advertise with you. Again, I check this site monthly.
Webhost – If you are have purchased hosting, chances are there is a lot of information that is being tracked there. I use HostGator and there is a lot of information on this site. Again, I pick out those statistics that I feel are most important for me such as the amount of visits and the unique visitors.