Previous posts here and here.
4th edition D&D ameliorates the daily powers problem in several ways. First, it has encounter powers, rather than having only at-will powers and daily powers. Encounter powers are really cool because they limit the use of a power without creating any of the problems associated with daily powers. With more powers being encounter powers, fewer are daily powers and thus the degree to which the characters get stronger by hoarding daily powers is reduced. Also, in previous editions you pretty much had to use up daily powers in a fight in order to make your character interesting (especially if you were a spellcaster). With encounter powers (and more interesting at-will powers), you can do interesting stuff every fight without needing to use your daily powers. This reduces the pressure to use up daily powers and the desire to renew them as often as possible.
4th edition D&D also has “milestone” powers like action points and magic item dailies, which are recharged with the number of encounters you face in a day. This makes it slightly easier for the characters to keep going during a day rather than rest.
A change which I find very helpful in giving the players a structure for how often to rest per day is the healing surge rule. Healing surges address the issue of character healing, which is slightly different from, but closely related to, the issue of daily powers. I should discuss that more in a future post. But the key point here is that healing surges create a natural stopping point for the day – you must rest when you don’t have enough healing surges to go on. Healing surges in general cannot be spent without limit during a battle, and are (for the most part) only spent to recover from monster attacks. So they cannot all be spent in one battle, and (ignoring certain powers) there isn’t really any incentive to try. This creates a natural flow for the game, where you adventure as long as you have enough surges, and spend your daily powers evenly over that time.
None of these changes, however, actually remove the basic problem. It is still most efficient to fight only one encounter per day. The changes just lessen the problem and make the regular solutions easier to employ. It seems to me that the rules work best when the characters choose when to rest, but have a strict time limit for the adventure as a whole. So now, whenever I create a D&D adventure, I put a time limit on the adventure. Usually my rule is that if you finish with only one extended rest, you gain maximum success. If you take two extended rests, you gain partial success. This sort of constrains the adventure design, but I’m happy with it right now.
The whole idea of “adventuring by the day” is rather D&D-centric. For other RPG’s I prefer to make adventures using the Torg concept of dividing into Acts and Scenes. Then you don’t have to worry about all of these nitpicky time details.