At the german subforum new users often confuse the ranks (“Super Senior Member”, “Elite Member”) for the usernames. Since their use is about zero (a user with a lot of not exactly helpful posts becomes a “Elite Member” very fast), I suggest to disable them.
If the software doesn’t allow this, but does allow custom CSS, maybe you could add the following line to hide them in postings?
.usertitle{display: none;}
Just looked it up: ranks can be disabled if we want to.
I agree that ranking based on the number of posts isn’t very helpful. So we can disable it but we can also decide to use a different reputation system to get some sort of ‘authority’-ranking system, or a post “thumbs-up/down” system?
Two examples of forum modifications:
Post ranking: http://fluxbb.org/resources/mods/a-very-simple-post-rating-system-with-thumbs/
Reputation system: http://fluxbb.org/resources/mods/another-reputation-system/
What do you and other forum members think?
I like the “post ranking” idea even with these ugly thumb icons 
I like marking posts as useful (or a kind of “thank you”). The second plugin seems to be “useful”-only and displaying a overall user rank. Not sure which is one is better. I slightly would prefer the second, on first glance.
But I could also imagine some people not liking such ratings for posts.
Negative ratings are bad, please don’t add them. “Thank you” buttons are ok, if they won’t take a lot of screen space.
What do you mean exactly? Negative post ratings or negative user ratings? I can agree if you mean the latter (the second option)…
Both. Who would like their post to be graded negative?