i usually cut chicken in strips for stir fries as well as beef and pork and lamb in no particular fashion. but of late i'm very into tender meat and want to maximize on it by making sure i'm cutting it right before i do anything with it.
it's an assumption that when you cut against the grain you're cutting and breaking the connetive tissue thus making the meat seem more tender.
You do not have to always cut beef across the "grain". With tender cuts like sirloin or tenderloin, you can cut it as you wish and the meat will be tender to the tooth. Cuts such as flank, and various cuts from the round need to be cut across the grain of the meat fibers for "tenderness". Other meats don't require it.