Is it possible to mark a post as spam?

You’ll probably want to read this to understand User Roles and capabilities. The highest level you want people to access (excluding yourself) should be Contributor. This way, the only person that can publish a post is you.

You may also want to look at a few of the plugins suggested at the end of the page.

If you absolutely need to allow users to publish their own posts, you may want to look at WP-Report Posts or GD Broken Report (just tinker around with the plugin’s wording to change it from “Report Broken Link” to “Report Spam.”). This way, users could report posts as spam.

Then, I would get a plugin like WP-Ban and ban the spammers by IP.