As far as I know, Lovecraft's works have recently (like within the past few years) entered public domain. And there are several websites out there that have his stories. I'm not sure about the status of his "revision" stories, like Curse of Yig, but since these tend to be less popular I doubt that anyone is hoarding up the copyrights. More recent stuff, like that created by Campbell or Lumley, would still be copyrighted.
Originally, Arkham House (created by August Derleth and Lin Carter) had the rights to the stories and sort of kept them alive. They gave Chaosium license to use it in an RPG. Now that the stuff's public domain, anyone could use the Mythos, they just couldn't connect it to Chaosium's game. You may also notice if you go to the bookstore, there's now several options for Lovecraft reprints (even stuff like Penguin Classics), whereas usually you could only get Del Rey (at least back in the eighties when I was buying them all).
The only time I'm aware of that any kind of legal action would've been taken regarding Mythos elements used w/o permission is with the original 1st edition of Dieties & Demigods, which had but Cthlhu and Elric gods in it. I don't know all the details of the story, but general consensus is that TSR had to reissue the book without them because Chaosium had the license to RPG material.