The only way to get rid of all advertising on our free hosted WordPress.com blogs is to purchase an annually renewable No-Ads upgrade.
WordPress.com has been running advertising on our free hosted blogs since 2006. Many bloggers do not know this because despite the fact they ticked the box required to get a free blog, they did not read the ToS. Many also do not read features page, or advertising entry in the support documents after registering their username and blog(s). Also note that as the ads do not display to us when we are logged in, and as many use browsers with ad blockers when logged out, they may not realize they are there at all.