Adapted from a post at gruntledluddite.wordpress.com
We often hear laments about grinding (also sometimes referred to as "treadmilling")—having to complete tedious and/or repetitive tasks. Various workarounds have been proposed and/or implemented (see some examples).
Completely removing the potential for grind would mean completely changing the leveling systems (which are otherwise tried, true, and effective), so the approach de rigueur is to include some sort of payoff; a gold star for having defeated 100 swamp rats. This is applying an extrinsic reward to either motivate the player to grind, or to placate them after a period of grinding.
While some aspects of game design—like the diminishing returns of experience points/leveling, and the random reinforcement of loot drops—are heavily informed by psychological findings, similar findings about the poor motivational effects of extrinsic rewards seem to have been passed over. Of course, it may also be that figuring out how to tap into intrinsic motivators is not only difficult, but getting back into the "overhaul the whole system" approach, which isn't what we want.
I find myself wondering, though, if this is a case where the old adage "you never understand the solution until you understand the problem" applies. We have a definition of what grinding is, but maybe we need to consider why grinding is off-putting to so many players. Think of your favourite RPG—whether it's Ultima, Diablo, World of Warcraft, or even Pokémon—the parts of the game that are perceived as "grinding" aren't mechanically different to the rest, they're when your goals are different. You need to get stronger before you can overcome the next boss. Your character still levels while completing quests, but it's a side-effect. "Grinding" is when leveling up becomes the main goal. And that's just not very interesting*.
We can see something similar in the world of sports. The equivalent would be playing a match that has no impact on which team wins the trophy, so the only advantage to the players is the potential for improving their stats (though there's still ticket sales, broadcast revenue, etc. to entice the higher-ups). For example, the fifth match of a best-of-five final when the score is 3-1; such a match is referred to as a "dead rubber", and in some cases is abandoned.
Maybe this perspective can help. Grinding doesn't seem like grinding if there's another reason for doing it besides boosting stats**. Earning a gold star doesn't help, unless it makes a difference to later gameplay. Perhaps NPCs could start referring to your character as "Bane of Swamp Rats". Perhaps swamp rats become more likely to flee rather than attack. But something beneficial—give them a reason, not an arbitrary number.
* For most players, anyway. For some, it's the main attraction, and that's fine, but I don't believe that's the case for the majority.
** It could also be an issue of granularity: the problem isn't that there's no other reason to kill all those swamp rats, but that you have to kill so many before it matters. It comes down to the same thing though: if you make the player's actions feel meaningful, they're less likely to get bored/frustrated with their progress. Use "breadcrumbing" (a trail of small markers/rewards to lead the player onward).