To include only academic titles in business cards of researchers with many positions?
I am thinking to exlude all positions, and just having your academic titles because I do not want to carry a pile of different business cards and in many languages


That seems like a somewhat bad idea. The main goal of a business card is to serve as a reminder for the recipient of the card who you were once the conference or event where the card was given out is over. Hence, the more specific the information on it is, the better. "PhD" or "MD" usually carries really little information, as many people at the events that you frequent will have the same titles. "Works at IBM" or "Associate Prof at UCLA" is much, much better in that sense. Your job title(s) are also a much more fine-grained representation of your seniority than your academic titles. The holder of a PhD can be anything from a freshly-minted graduate to a senior professor, while saying "Associate Prof" transports a lot more meaning.

Further, many employers will actually not be thrilled about you rolling your own business cards. Employers typically have a specific corporate identity, and expect you to use that (and not mention your other gigs on their cards). 

So what do you do?

Get separate business cards for all your major affiliations. These may include all your titles if customary, and only the job title and branding of this specific affiliation. You probably don't need a card for company X just because you are in the advisory board, or for university Y because you teach a course as external lecturer once a year. If you have multiple major affiliations, decide who you represent in any specific event, and use these cards (a good proxy for this might be who you are charging the event to, time-wise and financially). You can always verbally add your other major job(s) when handing out the card.