To off-set the costs of providing free hosting to millions of bloggers, 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 the 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.
10. Advertisements. Automattic reserves the right to display advertisements on your blog unless you have purchased an Ad-free Upgrade or a VIP Services account. http://en.wordpress.com/tos/
If the ads you see are found at the end of blog posts then provided you see this small About These Ads link what you are seeing is WordPress.com generated advertising.
WordPress.com does not use text enhance or text link ads or pop-up ads or links in comments. If you are seeing those then that's a browser-ad-on issue, or in some cases, it's embedded into free games downloaded from the internet. See here: Bloggers: Beware of Adware.
If what you are seeing whenever you save or update a post or page is an automatically added code/script block at the end of posts and pages that you can't delete then see here: Malware Targets Macs and Windows PCs
If you feel an ad is inappropriate please take a screenshot of it, upload it via Media -> Add New to your Media Library. Then return to this thread to post the file name to let Staff them know it's there for them to view.
Lastly, note to eliminate all advertising on our free hosted WordPress.com blogs we can purchase an annually renewable No-Ads upgrade.