Without a stats software you may never know about the health of your website. I mean how much world is interested in your website, how many visitors etc. There are many softwares that let you to have a stat for your website. such as google analytic, slim stats etc.
But tracking the AdSense Ads is a little bit different and looks difficult in first thought. There are many softwares available such as adlogger is a best example which can track your adsense ads. But non of thrid party softwares will give you 100% accurate results.
There is a built-in feature in your adsense account which is called as a channel. Channels are very easy to implement and use. You can keep an eye on each of your individual AdBlock on your pages. Just create a channel and assign it to an adsense ad and use it on your website. Whenever you will logged into your account you will see the results individually for that ad.
Lets say i have an adsense unit at right panel and 1 at the top of the post and 2 in between my posts. I can have a view for all of these ads, how much time they are viewed, how many clicks on each ad and how much CTR and ECPM each ad is giving me.
You can implement many channels to suit your requirments and use them with your ads. Channels are really an easy and effective way to track your ads.