I just received a /24 IPv4 network from my ISP. This very same /24 network was previously used by some hosting provider and if I made a quick scan of those 256 IPv4 addresses agains some DNSBL databases, then many of the addresses were listed there. This made me wonder are there other such public databases for different threads than spam? For example maybe some CERTs or other organisations have such (public) databases where they list IP addresses involved in botnets or hosting (regularly) web-servers which serve malware.
The MXToolbox blacklist checker is a good place to start.
You can follow that up by reading some of the lists hosted at iblocklist.com particularly including the dshield list, and then some of the others.
Robtex is an online tool that will give you various information about an IP or netblock. I prefer the "old robtex" version of the site, which is still available at the top next to the other links. The other linked resources will also have useful information from those vendors (McAfee, Google, Virustotal, etc.) about their perception of your netblock.