You can embed videos from many video services on your WordPress.com blog for free. Upload your video to any of these services and then embed it on your site by following these instructions: YouTube, Vimeo, Hulu, Flickr, Animoto, DailyMotion, Viddler, Blip.tv, TED Talks, Educreations, Instagram, AolOn, Vine, and Videolog.
If you want to upload and host your video files on your blog, you can do that with the VideoPress upgrade. VideoPress is priced per year and per blog. You can purchase it from the Store panel of your dashboard.