WordPress.com Pros:

Convenient all-in-one solution.
Just get a WordPress.com account and you’re good to go. There’s an excellent selection of themes to start with.

More stable and secure than self-hosted.
WordPress.com will have better servers than you, and will maintain & update the software so it’s more stable & secure than a self-hosted installation. Traffic spikes will not take your website down.

Cheapest solution.
WordPress.com is the cheapest solutions. Low annual fee to map your own domain if you so choose. Some (paid) features to customize style and prevent advertising.

WordPress.com Cons:

Limited design choices.
Changing how your blog looks is limited to a number of themes and their built-in features.

No extensions.

If you need specific functionality or to add special code, look into hosting your own WordPress.org software.

Less autonomy.
Automattic, the company that created and manages WordPress.com, will have it’s own policies that you wouldn’t have if you were self-hosted.