We don't allow plugins on WordPress.com for security reasons. Plugins are a feature only available for self-hosted blogs provided through WordPress.org.
To clear up any confusion, WordPress.com and WordPress.org are two different entities.
Please check out the following links to learn the differences.
We do offer tools for helping to make your WordPress.org experience as awesome as WordPress.com. Jetpack supercharges your website with features like easy video embedding, stats, and Twitter and Facebook sharing tools. VaultPress provides realtime, continuous backup and scans your website for security and performance. More information on both can be found at these links: