Orryyrro: ...
Yes, there is definitely less grinding today, at least in the sense of direction to what you are doing. Dungeons and Dragons Online for example has almost no grinding, being nearly entirely dungeons, with a lot of choice in what to do at any given level, or even World of Warcraft's quests give at least a semblance of a purpose to the grind. Meridian 59 and other older games have a lot less direction, and as there is a rather harsh penalty for dying the safe route of progression tends to be to kill the same easy enemies repeatedly until you are stronger. There are quests and the like, but they are much fewer and you tend to not want to risk your possessions by doing something that might be dangerous.
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Mentalepsy: ...
You know those half-hearted side-quests that you can pick up from the messages boards in The Witcher and Dragon Age, but probably ignored because they were pointless and boring? That's the replacement.
orcishgamer: ...
It's better than that in some places. Even in WOW, that gets by mostly on its Skinner Box mechanics, they write story arcs, since classic they don't just let them hang either (damned Worgen questline).
So those "pointless quests" get tied together with an over-arcing story, if you're interested. Otherwise you can do one or two and let it drop.
Gear progression has gotten more social too, raids and party quests are for more than hardcore. Some MMOs reward serious pvp efforts and even tie them into the storyline.
The only grind in DDO is running the same, easy instance once a week if you want to craft a greensteel weapon. These are very nice, but not totally necessary.
Some MMOs will have a rich enough economy or some other sidesystem that you can run your own meta-game (the lack of an auction house in Lineage 2 eventually turned it into a meta-game for me, I had loads of gear none of my toons could wear, just from trading I became obscenely rich - I actually did the same on a fairly broken server in WOW, it became more fun to run the AH economy than play the game).
You look at games like Free Realms or Wizards 101 (I know, I know, kids games, right? sadly superior in some ways to our adult games), you have CCGs in game, cooking, racing, pet raising/training, pet breeding, etc.
Thanks for the answers. So, to sum it up: Open worlds and dying penalties can result in mindless grinding. Levelling monsters, no penalties for dying, real multiplayer missions and some kind of story arc embedding result in a feeling that it is not so much grinding anymore.