As per the support page of wordpress.com, ads which help you earn money through your free blogs are not allowed on free wordpress.com blogs. This means, if you have a blog such as www..wordpress.com, you are not allowed to add any form of advertisement in it.

Yes, there are ways, if you require to add adsense or any other advertisements to your blog.

1. Ad control feature of wordpress.com is for blogs which have high traffic of more than 25000 hits per month. In this feature, you need to share your 50% revenue with wordpress.com You can use the form at this page  to apply for ad control feature.

2. If you are managing your own wordpress installation, you are free to run any ads.

3. VIP blogs are allowed to run ads. VIP blogs are blogs which pay a flat rate per month fees to wordpress for getting the hosting and all other benefits. Some of the VIP blogs, as per wordpress.com are, allthingsd.com of Dow Jones, politicalticker.blogs.cnn.com of CNN. VIP hosting  is allowed only for the companies, which wordpress has confidence in. If you are getting more than one million hits per month on your blog, you are a candidate for VIP blog hosting.