I'd think I'll post on the other side of the coin, under which circumstances I'll avoid a quest unless there's a very good reason for me to do so.
I can think of three examples in which this happens.
1. Collect an arbitarily large number of items. 10 is okay. 100, or 200 would be effectively grinding at mobs / repop locations.
2. Placing a lot of emphasis on high random drops. Maybe you need Item A, B, C, D for this quest, but they are all random drops with a low chance of happening. Completing this quest would also be grinding at mobs, with some emphasis on luck as well.
3. A large number of DTs. (debatable, I'm sure) This really isn't a problem here, as DTs are clearly highlighted. But if I'm doing a quest, and every other room I walk into are DTs without any kind of warning, I'd be pretty pissed off.
Well, basically, these above types of quests have something in common. The player who spends more time playing will eventually solve this quest, regardless of whether he hacks and slashes his way through, or spend some time thinking about it.
*Edit. Come to think of it actually, 1 and 2 are just variants of the Questmaster kinds of quests. Issue you a quest to slay this mob or recover an item, and then get QP. After getting a certain number of QP, you could trade it in for equipment. But then QP would be equivalent to the 'number of items' to collect in 1, and the 'number of kills needed to get an item' in 2.
Perhaps it's just me, but I feel that if a quest doesn't let you exercise your brain cells a bit, I'll tend to skip it, unless I have nothing better to do, or the reward is kind of worth it. However, I don't think 4 Dimensions have these kind of quests