Grinding is only fun if there's a tangible goal in mind (a chance for an upgrade). If the game doesn't reward grinding, it better have something else to keep the players attention.
If a game is built around grinding (in that it makes grinding rewarding) then i'm more likely to enjoy the grind, but if the game doesn't place emphasis on grinding (no significant punishment for not grinding, or no significant reward for grinding, or both) then i'm less inclined to grind in general.
Games not built around grinding are usually story driven. Legend of Dragoon, Skies of Arcadia, etc. are more about progressing the story and don't really give significant rewards for grinding. Leveling up in one area may make the upcoming boss a bit easier but that boss isn't too bad even if you just run into them without fighting more battles than necessary.
Games built around grinding usually require that you grind in order to progress. Ragnarok Online is a good example. There is no 'story' to speak of. You make your own based on your interactions with other players. In order to really progress, you need to find upgrade cards, slotted equipment, and grind a LOT of enemies. A lot of classes involved kiting a bunch of enemies and one shotting them with a powerful AoE attack. Similarly, boss monsters usually dropped some of the best loot and upgrade cards, and took teams that were built around taking them out in order to defeat. They had both paper-grinding and metal-grinding in that game, but you needed to do a lot of paper-grinding before getting to the metal.
I'd call myself a paper grinder, just because I like the feeling of watching a bunch of enemies drop at once and seeing a bunch of loot drop at once. In Ragnarok, I built characters that could take out a horde of enemies at once, since the game was designed such that each enemy had a very low (0.01%) chance of dropping their cards. By taking this approach, I could get more cards than by taking out tougher enemies one at a time (even if those enemies dropped more valuable cards).