This is a broad ranging question and can probably only be answered with the same sorts of brushstrokes. Ultimately, it comes down to what you, the user, wish to protect.
Fundamentally, you should not post anything that would allow someone else to find it easier to compromise your system, or any of the other connected tools or accounts you use. For this reason you should consider:
- Scrubbing any passwords from any material that you post
- Obscuring your IP address
- Changing details of ports you open to the net
- Removing details about your ISP
- Redacting your personal email address if you don't wish to attract (more) spam
- Changing or removing hardware identifiers like MAC addresses
The real risk is not necessarily around the individual pieces of information (except, perhaps, in the case of your password—especially if it is one that you reuse, but you wouldn't do that, of course), but in the aggregate that some malefactor could piece together with some time and effort1.
Of course, it is not just about technology or your system; more broadly interpreted, there are other prophylactic measures you may wish to consider.
If you value your privacy, and that of your family, then you would want to take additional steps to ensure that only that personal information that you are comfortable with enters the public domain; for example your geographic location, full legal name, photograph or further identifying information could all constitute material that could be used for identity theft or other nefarious activity.
These other facets of information are unlikely to be included in screenshots or logfiles, but if they are already online through other means, such as social networking sites and the like, then it does increase the surface of vulnerability and, in any event, you should be conscious of that profile, at the very minimum.
1. Standard levels of paranoia being applied...