Some games, the grind is part of the game itself and quite enjoyable - Diablo 3 is an example of that, it's got a very enjoyable gameplay, lots of endgame content and goals, etc.
FFXIV... meh, can't be arsed anymore. As long as there's achievable goals (like you can tell you only need to do X more) then it's fine, otherwise, cba.
With Eve Online, it depends. Mining is one of those things you just turn on and can leave for a couple minutes, just alt-tab to reddit or wherever. Other activities just involve waiting for a week (PI), and then there's PvE combat; missions are a grind, but they involve shooting and paying attention, and Incursions are group activities, you need to stay focused on that - do everything right and you'll earn a hundred million / hour if not more, with barely any time to think. There's voice chat and banter involved there too, so there's that.
With the FF games, I think most don't require grinding as long as you follow along at the pace that seems to be indicated by the game (speaking mostly for the later ones, mind you, IDK how it is with FFI-VI exactly; I know I did fail at VI because I was underleveled at the time, should find the arsedness to go back to that one sometime). I did do most of the content for FFX, which probably did involve some grinding - but I had a cheat sheet there, which helped me get the exact goals I was working towards. (yes I did the 200 lightning dodges)