If you want to upload and host your video files on your blog, you can do that with VideoPress, which is included with WordPress.com Premium and WordPress.com Business plans. Full instructions for adding and playing your videos can be found on the VideoPress support page.
You can also embed videos from many video services on your WordPress.com blog for free. While videos from many popular services will embed automatically by simply placing a link to the video in your post or page, we also have detailed help for a number of video sites:
- CNNMoney Video
- The Internet Archive
- TED Talks