Cthulhu is the most famous and therefore is the most popular. He also is one that seems most like a Giant Monster, as the others are more entity like and Cthulhu is a Mountain sized Kaiju-like monster, and he seems different to the others as he is more mythical and in some ways more intriguing.
Yog-Sothoth is interesting as a God-like Character and he knows and is all, which makes him a lot like the Christian God (or any Religious God) and how he is everything and knows everything which makes you feel very insignificant. Also, he is Amoral, which makes him, in a way, more interesting than the Religious God as he doesn't care about you but doesn't hate you either.
Azathoth is an epic concept as he is Omnipotent and created everything, but he is also mindless and he created everything in his dream, which is very unique and thought provoking. Additionally, the fact that all of existence and things like speed, strength and destruction is simply a concept created by him is interesting as well and as he could destroy everything by awakening from his dream is simply terrifying.
Nyarlathotep is interesting as a villain and a very evil, devilish like villain, probably in my opinion the most evil villain in all of fiction. He is a God who abuses his powers to cause suffering to humans for the fun of it, as well as causing trickery and mischief which makes him a somewhat immature god.
Change in mine, Nyarlathotep. At least he has hands. Yeah, Shub goes and chills when the rest are off doing. The word on Lovecraft seems to be that he gradually forgot about all the others in his appreciation of Cthulhu, there's even the thought that they are all alternate names for Cthulhu.
John Thiel wrote:
Shub Nigurath is who I like best. He's quieter, keeps to himself, mysterious.
Shub-Niggurath is a female, not male
That's an interesting point and raises some interesting philosophical questions. I guess Shub-Niggurath is generative, and has some female attributes, but I'm not sure binary human sex categories really have any relevance with these elder gods (if they have any meaning apart from culture in general). I suppose its my own unconsious bias that defaulted to male. Some of the sources indicate parentage and assign sex and sometimes gender to the various entities of the Mythos, but I'm not actually sure if it's ever applied uniformly or ultimately can be given much weight in light of the cosmically unknowable aspects of these beings. There's a handful of indications that some of the entities may be self generative/asexually reproductive (Abhoth), hermaphroditic and/or sexually fluid (Nub and Yeb). All of these have wholly terrestrial real-world analogs that make this a very reasonable possibility.
I've picked up this discussion further in a new thread. Here
Yog-Sothoth, first, last and always. Although I retain great affection for both Yidhra and Zulchequon. Deities of knowledge, evolution/survival, and the darkest despair...what else do we need in this cataclysmic age?
Yidhra, First of Her Name, Mother of Darkness, Breaker of IPhone-Chargers, Eater of all Life-Forms, Queen of the Earth, Mother of Friends With Alcohol Tolerances, Champion of Lip-Cup, Blood of High Sodium Level
Kthanid hes the inverse and twin of Cthulu and while hes not very similar to him, or Hastur he still has an intersting way of enacting his will. Also he suppsoedly despises "evil" which while isn't my favorite thing about him does admitiddly add to his intrigue. He banished The Great Old Ones but is still either unable or refuses to inact violence on others.
In short "Good Guy Cthulu" ; Never thought I'd say that.