As part of my discussion on the iconic picture of the 3e iconic D&D party getting their tushes handed to them by Cthulhu (albeit a small-sized one) there was some discussion about whether or not Cthulhu is "deity level" in D&D, or what, exactly he is. My own point of view is that assigning this kind of heirarchy is antithetical to Lovecraft's design (although it was done by Derleth, and followed by every RPG company that ever featured any kind of Lovecraftiana since.) But if you have to do it, the only deities are really Yog-Sothoth, Shub-Niggurath, Azathoth and Nyarlathotep. Guys like Cthulhu, Tsathoggua or Hastur are better represented as equivalent to the archfiends, if you will. Demon-lords.
But let's look at his stats in the various D&D versions over the years.
In the d20 Call of Cthulhu book, he's a CR 34 monster, although it was an early 3e era book, and I'm not sure that I'd consider that CR to have been "trued up" very well. However, for the sake of argument, let's say that it's more or less accurate. If so, the Demonicon of Iggwilv gives demon lord stats of high twenties to low thirties--Demogorgon himself showed up as 33.
In Paizo's Bestiary 4, they included Pazuzu, a demon lord, and Cthulhu. Both came in at CR 30.
I think these latter stats are about right, and the perspective of Cthulhu as a "peer", if you will, of guys like Dagon, Orcus, Demogorgon or Pale Night is about right. Given the overtly Lovecraftian description of the obyriths anyway, this is a good fit. There's actually a case to be made that Dagon and Cthulhu are the same, as it turns out. Dagon, of course, has a former mythological life of his own as a Philistine god, as well as the "star" of two of Lovecraft's stories, his early effort "Dagon" and his masterpiece "The Shadow Over Innsmouth." There is a great deal of overlap in terms of how Dagon and Cthulhu are presented in the Mythos, and there have been several postulates that "The Call of Cthulhu" was, in fact, a rewrite and reimagining of the earlier story "Dagon", and the two of them are in fact two names for the same being.
In the d20 Call of Cthulhu book, of course, Dagon and Cthulhu have separate write-ups. But, by definition, all of mankind's attempts to characterize the Mythos are incorrect--the only reason we can't correct it is because we don't know where its incorrect. As it happens, I think the conflation of Dagon and Cthulhu makes a great deal of sense.
And since Dagon of D&D is overtly the same as Dagon of Lovecraftiana (complete with the worship of kuo-toa "Deep Ones" in weird seaside towns, riffed almost word for word from "Shadow Over Innsmouth") that means that the CR 30 (or 32, or whatever it was exactly) Dagon from the Demonomicon of Iggwilv series of articles in Dragon Magazine can be stand-in stats if required. And if you want a lower CR version, for whatever reason, there's one in the low 20s in Fiendish Codex I: Hordes of the Abyss.
In the end, though, what does all this matter? It doesn't, except as an interesting point of reference. I can't imagine that I'd ever really have my characters "fight" Cthulhu or Dagon, or any other demon lord, archfiend or god. That's simply not the kind of game that I'm likely to run. If I use d20, then I also use E6, which means that even the low-CR version of a demon lord, at over CR 20, is way out of the league of the most powerful characters imaginable.