What rules guide whether to put qualifications on an academic business card? I'm just wondering what rules of etiquette guide whether an academic puts qualifications on a business card. I'm assuming that either "Dr" at the start or "PhD" at the end is important to include where applicable, perhaps with the exception that higher titles such as "Prof" would take precedence over "Dr".

However, what about beyond that?
The accepted conventions also depend strongly on country. As a general rule, though, I'd avoid anything "cute" unless you happen to be your own boss. 

For instance, in the US, I'd expect to see doctoral-level degrees listed. I'd also expect to see high-level professional qualifications, such as "PE" for "Professional Engineers." Similarly, if a master's degree carries sufficient professional weight in one's discipline, I'd list that, too. You are also correct in assuming that Prof. "overwrites" Dr. 

In Germany, by contrast, one is expected to list all degrees of equivalent standing, including honorary degrees. This can lead to rather unwieldy titles such as


  Univ.-Prof. Dr. rer. nat. Dr.-Ing. h.c. Dr. rer. nat. E.h. Johannes Schmidt


(Note: I've seen substantially longer, too!)

However, two additional points are worth mentioning. 

First, any degree at the master's or diploma level is considered significant enough to list as part of one's title:


  Dipl.-Ing. Michael Mustermann


would be expected for someone with a "Diplom" in engineering. 

Secondly, until recently, non-German degrees were not considered the equivalent of German degrees. An American doctorate holder was 


  Joanna Doe, Ph.D.


and was legally not allowed to call herself


  Dr. Joanna Doe 


However, this has been somewhat relaxed recently, although only for degree holders from certain countries.