Problem with most grinding systems is that they replace game-play instead of compliment it.
The idea, and I suppose there can be debate over this, comes from old pen & paper role-playing games like Dungeons & Dragons. The whole point is that it's supposed to represent a long-term journey. The classic role-play gamer appreciates the idea of 'building' a character for 6 or 12 months. It used to take months upon months to level-up in old pen & paper RPGs, and if you ever played them for the purpose of reaching X level or achievement, it would be a silly and pointless grind. But no one played them that way. You played them because the game-play itself was fun, and it was cool to build a character slowly over 6 or 12 months.
The same intention translated into computer games, and somewhat was successful in some RPGs. You could say most of EverQuest's original 'value' was because it had such a grind. The whole experience was building up a character slowly over many months and the social interaction you had while doing it. The original idea for Ultima Online where you'd spend many weeks building a skill, a few hours a day practicing your blacksmithing, but not treating it too much like a means to an end.
Proper use of 'grinding' or any leveling system that 'could' be a grind is that you're never actually supposed to grind.The game should be playable on its own merits without 'grinding,' and then the leveling system is there to further add an RPG dimension to your character building.
Then, there has been some use of grinding, purposefully, to create a fake sense of achievement. This can somewhat work in some RPGs. I mean, I said EverQuest and let's be fair, no one would probably have played EverQuest that way without grinding, so it sort of fails that first test that I said. But most people that enjoyed EverQuest still enjoyed the grind because it represented a different sort of gameplay -- a gameplay not about the specific actions but what they represent. They give more meaning to your reward, basically. A lot of people that play RPGs want a sense of achievement from character progression, and slow grinds are one of the best ways to do that. There are people that enjoy and appreciate that, so that's why grinding is still a high demand part of MMOs and RPGs, if only for a niche of gamers.
The biggest problem is when games use grinding in games that either genuinely replace content or for gamers that don't care about grinding. You could say that original EverQuest passed these 2 tests. It certainly never 'replaced' content -- Verant would not have magicaly been able to make more content without grinding. They were already had 100% capacity for content. It just extended the current content. Which the gamers at the time wanted.
But there are games, especially console games, where it genuinely feels like the game development was lazy and used grinding as an excuse to not put more effort into content. Or, the game had no reason to have a grind. World of Warcraft somewhat struggled with this because it had a more casual crowd than EverQuest, and that is why it ultimately became less grind-y. Destiny seems to also be struggling with this a bit right now as obviously a lot of players in it right not dislike the grinding or leveling system for bosses, and it doesn't have the content (both in terms of quantity and quality) of a Warcraft or the itemization of a Diablo. In old Japanese RPGs, sometimes it felt like grinding did nothing but replace content, because there was low demand for grinding from a RPG player perspective (this was just a character you used for 2 weeks, not some personal character you wanted to build for 6 months) or because it genuinely felt like instead of adding a new cave or mountain before a boss, the game just forced you to fight the same slimes or bombs over and over.
You could argue a game like Shadowrun on the GENESIS was one of the best examples of old pen and paper RPG gameplay on a console. There was no real story progress, per se, though there were a few unlocks to progress the story to the final boss. But the game as a whole was mostly just grinding 'runs' to become strong enough to complete the very tiny story parts. And, if you played Shadowrun on the Genesis just to finish the story, it was a boring grinding game. But that's not why most people played the game. They play it, and hopefully some still play it (as I do) because it has one of the most fun 'random mission' systems in any RPG still to date. Even to this day (and this is in part to the 80s synth/cyberpunk-esque soundtrack by Tangerine Dream), when I do some of the Heists in GTA V, they remind me of and make me think about Shadowrun's mission system. You grinded in Shadowrun because it was just a blast to create a character, recruit a team, and then go raid or hack a MegaCorp's headquarters. It was incredibly grinding, objectively speaking, and almost every missions was repetitive, but to this day it's still one of the most fun 'grinds' in my opinion just because of all the other parts (the character progression, the music and atmosphere, the art) compliment the game so well that the 'grind' doesn't feel like a grind. It just feels like an old school RPG where you go into the game, decide what sort of mission you want to do for the evening, and go on a 'run.' In Shadowrun's case, it was a grind if you played it just for an 'achievement' like reaching a level or finishing the story, but if you played Shadowrun because you genuinely loved the gameplay, then the grind of it all complimented the gameplay with a great slow progression of character development.
The best grinding games I've played are games where I never feel forced to grind. I grind like crazy in FF Tactics, sometimes reaching Level 20 or 30 before the story even starts or progresses passes Chapter 1, just because leveling and fighting in that game is so fun. I grind like crazy in Diablo games before the item progression compliments it with small 'dings', and I grind like crazy in old MMOs because as an old school RPG player, I appreciate the idea of joing a MMO community and building a character, persona, and community over 2-3 years. The 'boring grinds' of skills in UO and SWG are, to this date, still the best world/community fostering gameplay I've ever seen in a computer game, and by far the closest I've seen a game genuinely establish a real virtual community and lifestyle. I remember grinding Cecil and Kain to like Lv17 or something, which took hours upon hours, in FF2(IV) before that first Titan fight, just because I wanted to see if I could survive, and I remember grinding 4 months 24/7 to become the first High Warlord Warrior on one of the biggest WoW PvP servers because I loved the lore, community, and setting of Warcraft so much that I just 'wanted' to my character to be 'that character' -- a High Overlord Saurfang type of character. I even wrote journals and blogged role-played pictures to 'craft' that 'war story'. In the same way, we used to play D&D every weekend for months, slowly crafting and building up a character in old pen & paper RPGs. All of these things could have been perceived as grinding, or felt like grinding if you didn't enjoy the gameplay and just wanted to 'ding X'. But the negative parts of grinding were not something I felt when I personally did them. For me, it was just great RPG character progression. So, there are games, for certain types of gamers, where grinding can work as a tool for 'character story', if you will -- a way to add an extra measure to who your character is and what they're achieved.
But there have been a lot of games, too, where the only reason I did it was because I felt I was forced to do so to progress the story or only because there was some interest unlock behind a certain 'ding.' And there have been a lot of other games where, even if I enjoyed the grinding, I felt like it didn't suit the game or the vast majority of folks playing it.
