The Dshield project
The Dshield project is maintained by the folks at the Internet Storm Center (https://isc.sans.edu) and allows participants to forward their (anonymized) logs to a central repository where they are aggregated to provide a good picture of "what's happening on the internet."
Specifically, the information that is forwarded is the connection attempts that are blocked by your firewall. There is also a dedicated Dshield sensor that can be used if you don't want to use your actual firewall logs. Instructions for participation can be found here: https://isc.sans.edu/howto.html.
This aggregated data gives us a view of what ports malicious actors are looking for, intending to exploit them. The participant's addresses are the information that is anonymized. The various high-level reports can be viewed here: https://isc.sans.edu/reports.html.
In particular, you can drill down into any of the "top 10 ports" on that page to see activity...