Lovecraft's major inspiration and invention was cosmic horror, the idea that life is incomprehensible to human minds and that the universe is fundamentally alien. Those who genuinely reason, like his protagonists, gamble with sanity. Lovecraft has developed a cult following for his Cthulhu Mythos, a series of loosely interconnected fiction featuring a pantheon of human-nullifying entities, as well as the Necronomicon, a fictional grimoire of magical rites and forbidden lore. His works were deeply pessimistic and cynical, challenging the values of the Enlightenment, Romanticism, and Christian humanism.
Non-human influences on humanity
The beings of Lovecraft's mythos often have human (or mostly human) servants; Cthulhu, for instance, is worshiped under various names by cults amongst both the Eskimos of Greenland and voodoo circles of Louisiana, and in many other parts of the world.
Civilization under threat
Lovecraft frequently dealt with the idea of civilization struggling against more barbaric, primitive elements. In some stories this struggle is at an individual level; many of his protagonists are cultured, highly-educated men who are gradually corrupted by some obscure and feared influence.
Race, ethnicity, and class
Lovecraft lived at a time when the eugenics movement, anti-Catholicism, nativism, and strict racial segregation and miscegenation laws were all widespread in the United States and the Protestant countries of Europe, and his writings reflect that social and intellectual environment. A common dramatic device in Lovecraft's work is to associate virtue, intellect, civilization, and rationality with upper class White Anglo-Saxon Protestants. These are often posed in contrast to the corrupt, intellectually inferior, uncivilized and irrational attributes which he associated with both the lower classes in general and those of non-Anglo Saxon ethnicity, especially those who have dark skin. He held English culture to be the comparative pinnacle of civilization, with the descendants of the English in America as something of a second-class offshoot, and everyone else below.
S. T. Joshi notes, "There is no denying the reality of Lovecraft's racism, nor can it merely be passed off as 'typical of his time', for it appears that Lovecraft expressed his views more pronouncedly (although usually not for publication) than many others of his era. It is also foolish to deny that racism enters into his fiction." In his book H. P. Lovecraft: Against the World, Against Life, Michel Houellebecq argues that "racial hatred" provided the emotional force and inspiration for much of Lovecraft's greatest works.
Native America & Speculative Fiction: Interview with Amy H. Sturgis
For more on the subject, see The Best Indian Books.