Does beer really go bad after the 'best before'-date? Does beer really go bad after the 'best before'-date?  

I hear I can drink beer even after the expiration date, but is it safe and does it still taste good?
The beer will not be bad in the sense of unsafe to drink, since no harmful pathogens grow once the beer is fully fermented. So you can certainly drink the beer.

However, the beer may not taste good! Over time, the beer will oxidize, both from oxygen introduced during packaging, but also through the release of oxygen from compounds previously oxidized in the beer. The oxygen causes the beer to stale, producing tones of sherry, paper, cardboard. Hop aromas are muted, and hop beta acids oxidize to produce an unrefined bitterness. Other forms of staling can lead to a soap taste.

Generally, the higher the alcohol content of the beer the less you need to be concerned with the use by date.