First, DaveL and charlatan75 raise a top-level question: what is the problem with clerics, and is it really their problem, or a problem with the magic system as a whole? I'll take the question about D&D's magic system first: I personally have no problem with the magic system, because it's pretty simple (you get X spells per day, you can't cast spells more powerful than some number based on your level, and there's a prep ritual you have to go through,) and also it's really not that bad a model for many varieties of fictional magic. There's a lot of wiggle room to make a particular spell system feel different from other spell systems and fit a particular setting. My only real problem with the D&D magic system is that, over time, all spell lists move towards the M-U spell list, making all magic feel the same. The solution to that is to be rigid about exclusions from the spell list: prevent Magic-Users from researching pure healing spells, and restricting Clerics to a few simple support spell types; also, try moving out of the comfort zone when varying other spell system details: determine "X spells per day" in a dramatically different way, instead of just saying "it's based on a different attribute!"
So what is my specific problem with Clerics? It's not really that they are too powerful in an absolute sense, but that they look awfully good in comparison to other classes. Functionally, they are between Fighters and Magic-Users: they fight better than M-Us, but not as well as Fighters, and they cast more spells than Fighters, but not as many as M-Us. So, either they are M-Us who have traded some magical power for combat ability (plus Turn Undead,) in which case they should use the M-U progression, or they are a hybrid of the other two classes and should have a progression between the two.
Instead, they have lower XP requirement than either class. This may have originally been a social solution (Clerics weren't as flashy/desirable as the other two classes, maybe, particularly because of their limited attack capability, so XP requirements were reduced to encourage people to take the class.) One solution -- not the only solution -- is to change the progression; as I suggested above, I would just use the M-U progression, if I wanted to go that route. The other solution is to keep the progression, but limit their power a little more, to make it fit the by-the-book progression. Some kind of spell failure chance would fit that bill, which is what "Clerics Without Spells" is all about: making Cleric spells less certain by merging them with an existing Cleric mechanic, which simultaneously adds some distinctive flavor to Cleric abilities.
Second, Ed Green is concerned about lower-level clerics actually getting a power boost. They are certainly able to try some things they wouldn't have been able to do before, and can use their powers more often. Is it a boost? I think if you take into account that reduced chance of the spell working, it balances out. A 1st level Cleric can't turn a mummy, because they would need to roll a 17+ on 2d6 to get a Good or better result. And it's a 15+ to raise the dead, or 11+ to heal 2d6 damage, or 9+ to heal 1d6 damage. The 1st level Spell-Less Cleric can try more often than the Spell-Full Cleric, but won't necessarily succeed more often. Still, you can add a restriction that Healing wounds or disease and Dispelling or Warning against danger are restricted to half the Cleric's level, if you are concerned about the range of their abilities.
This leads into other options for restricting clerical power, for those who want them. Restricting spells per day with a piety attribute (per Pierce,) or linking spells per day to level modified by Wisdom (as suggested by Jim) are the two most obvious choices, as are penalizing multiple miracles in one day. I've proposed piety systems before, but I obviously simplified that for "Clerics Without Spells". You can include an automatic -1 Piety penalty after every prayer for aid, or every successful prayer, or only for prayers for the most powerful miracles within the Cleric's ability. You can have a reaction roll determine how many miracles a Cleric can perform each day before losing -1 Piety per further request.
I chose not to go with those options because I want Clerics to offer *lots* of short prayers. Secretly determining the deity's reaction (or the petitioner's wavering faith in an unseen divinity) means that the player won't say "oh, that didn't work? I must have used up my prayers for the day. I'll stop praying!" Each time a spell fails, it might be because of actual divine wrath, or it just might be because that particular request was just not part of the divine plan. The player has no way of knowing.
There are two restrictions I might add, though. One is that either a modified result of 2 or less or an unmodified 2 results in loss of piety. This way, even high level Clerics can fall out of favor, and even successful requests do not guarantee that the Cleric is in good favor. I'm not sure yet, but I may also base the amount of piety lost on a d6 roll, but with a maximum piety loss equal to the "power level".
The other restriction would be a non-cumulative penalty for multiple miracles, based on frequency:
- -1 if at least one prayer has been answered today ("Haven't I heard from you already, mortal?")
- -2 if a prayer has been answered within the last hour ("Indeed, I *have* heard from you. What is it now?")
- -4 if a prayer has been answered within the last turn ("You wear out my patience, mortal!")
Those options mostly fit my particular flavor and interpretation needs. "Flavor and interpretation" is also why I didn't include Blessing as a power. Just what do we mean by a blessing? Do we mean something mechanically identical to a Bless spell? I see no need for that, in terms of flavor. Or do we want something that feels like the blessings we see in Arthurian romance and the like? The way I interpret legendary blessings, they were mostly protective in nature, driving away evil and preventing harm. That's basically the Turn Undead, Defense, Command, and Dispel abilities. It might be OK to allow "pre-blessing": the old priest blesses you, and it gives you a one-time use of one of those abilities at the priest's level -1. This would be an easy way to implement holy water, for example.
There's a lot more that could be said on this subject, but I'm running on kind of long as it is.