Ads Easy is the most simple way to integrate some banners into your blog. It works with basically everything and is AdSense optimized.
If you need to place some Advertisements on your blog, but you don't need other stats, than those from your adprovider and you don't want to have ads in your posts, this is the solution. You can define the widget style yourself or you can leave it to your theme. Show your ads on every type of page or just on the frontpage. Keep your registered users adfree when they are logged in if you want. If you use Google AdSense, you can wrap the AdSense tags automatically around your loop, header, footer and / or sidebars. In the editor, you have a button appearing, that will wrap content in the Google ignore tags. Simply select some text and press the button, the shortcode will do the rest for you.
Ads Easy was tested up to WP 4.2. It should work with versions down to 2.7 but was never tested on those.