Perhaps quests could be viewed from more than one perspective. For example:
First Perspective, Quest type
One time quests. These would be things like explore a mountaintop to kill a troll, kill a dragon, capture a pirate, seduce the daughter of a rival king, or any of the other great ideas discussed in this thread. The commonality would be that you would get this specific task only one time.
Repeatable quests. This type of quest you have the option of doing as often as you would like but they would end and have to be restarted if you wanted to do them again. For example, the hermit who needs seaweed gathered from the merfolk, the caravan which needs an escort, the tavernkeeper who needs you to hire a band for a dance, the barmaid who wants you to hunt down the bum who insulted her 'honor' or the frog who wants you to bring a princess to kiss him. Again, lots of good ideas in this thread.
Open ended quests. You could have this one running all the time. A businessman might reward you if you keep trade routes for his products open, a town may reward you if you keep their coastline free of pirates or the wood elves send you gifts if you keep the local orc population suppressed.
Second Perspective: Reward type.
Quest rewards should be enough to encourage the player to do quests but not so much that the game is unbalanced to where a player could ignore their economy and just quest their way to wealth.
Unique item quests. Getting a unique/rare item should not be a trivial task. Quests for such items ought not to be ones which are guaranteed successful. They ought to have some real difficulty and committment and risk. If something is easy to get then it is not valued, if we have to work for it then we care about it. Real life examples: graduate degrees, military medals for valor, significant recognition from community or workplace.
Character advancement quests. These might be such things as improved stats, a new skill, a new spell. Like unique items, these should not be trivial to obtain, especially at higher level/higher values. Ideally, the quest and the reward ought to have some logical relationship. For example, if we have to spend significant time hunting down Dread Pirate Robert, then (in addition to some loot from the pirate booty) our tracking or sailing skill might increase slightly. Examples might include better leadership for military related quests, endurance for quests in the wilderness or desert, knowledge for quests involving researching and searching, higher odds of producing children for quests asking us to successfully romance beautiful ladies, &tc.
Reward quests. Here we get the traditional monetary/fame/gear for troops type rewards for doing traditional quests. Escort the convoy and get paid, eliminate the band of goblins and get their weapons to give your next group of recruits, subdue the hillfolk and take over their lumbermill, clean the rats out of the slums and your city's health/growth rate improves, build a new monestary and your spell research is faster.
Faction/character quests. These might be specific to the faction you play and ongoing. They could influence various civilization wide characteristics and might also be tied into the character customization screens. In other words, as you create your character and determine the kind of person s/he is, you might also be opening up quests which would encourage you to play consistently with your character. The rewards would also be consistent with your character's traits and the quest. For example:
- Choose a 'good' type of character with a merchant's background (probably not undead). You could have two quests you could take. The first, dealing with your 'good' characteristics, would improve the loyalty of your population and armies as long as you released prisoners (rather than killed them), grant mercy to monsters you vanquish on quests, and treat ladies gallently. In other words, if you act according to your traits, you get additional bonuses beyond the character stats. If you don't, you would then get penalties. Continuing the example on the character's mercantil background, if you build marketplaces, establish trade routes, suppress bandits and do other pro-business actions, your tax revenues would increase even more than your merchantile background would give you as a base stat. If you don't, you would have a penalty.
So these quests would be ones which the character could take, at their option, and which would enhance their character traits but also bring the risk of negative consequences if not followed.