IMO, there should be five different categories of powers:
At Will: we know what this is from 4e.
Encounter: you can use once, and then you have to catch your breath before you can use it again. And, yeah, we know what this is from 4e.
Daily: you can use once, and then have to have a good night's sleep before you can use it again. We know what this is from 4e.
Always On: You activate this power, and it stays on until you turn it off. If you want, you can turn it on or off many times per day/encounter/whatever. (Probably need a rule that you can only have one always-on power at a time, but that you can switch them as a free action on your turn.) A good example would be the 3e Paladin's holy aura power.
Conditional: This power has some trigger condition. Whenever you meet the condition, you can use the power. (Again, you probably need a rule that if you have multiple powers with the same trigger condition, you can only activate one at a time.) A good example would be the Rogue's sneak attack.
I think that covers everything, although I do know 4e did have a couple of "use twice in the encounter" powers. I wasn't a fan. (Also, note that under this model a "class feature" is just a power that you don't get to choose.)
What is the general opinion?
Another way is like in Mike Merles Iron Heros. In that system martial characters gain tokens as they fight based on their actions (and sometimes the enemies) these tokens represent the fighter using his martial skill to manipulate the fight by maneuvering his foes into poor positions, or a berserkers growing rage, etc. You can then expend tokens to accomplish powerful effects.
My favorite 3e example is focus. It was implemented a few times, once as a psionic thing and (IIRC) in PHB II with a set of connected feats.
There are other ways too. For example what if rolling a nat 20, instead of being a critical hit, grants you an "Advantage" token for that fight which might be expended to cause double damage on an attack, or somesuch effect. And could additionally feed into class features/feats/skills etc.
I can tell you that I, personally, would much rather use an Iron Heroes style token system than a "Your fighter can use 'strike of the sleepy eel' once a day" system.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.