Grinding, in RPGs, didn't exist until they were converted to Video Game format. In the absence of a human 'Game Master' to make certain that challenges could be survived by the players, players would end up having to grind random encounters if an area was too difficult for their level. fortunately, most computer RPGs are well-structured, and as long as you don't run from every battle like a coward, your characters' level will usually stay high enough to face the increasingly difficult challenges with minimal grinding.
Unfortunately, MMORPGs decided to make grinding an important part of gameplay. Players would grind for experience, grind for rare items, etc. Theoretically, this is to make the game take more time, forcing the players to pay more money, as many MMO's, particularly early ones, require a constant subscription to continue playing.
Grinding could be replaced by something... FUN. Instead of performing the same task over and over and over until you want to smash your computer into pulp, you could make the players PLAY to get things that are supposed to be rare. Challenge players instead of making them suffer.