I think he's traditionally an SF writer but he's really more fantasy. My first exposure to him was in the third grade when a teacher (one of my two or three favorite teachers) read Tarzan to us for about a chapter a day. That remained a kind of singular experience until I came across a trove of my uncle's paperbacks (kind of weird in that he's not interested in SFF at all but apparently went through a Burroughs phase), which I read in a concentrated period when I was a kid. Oddly, he didn't have any of the Mars books so that's been a glaring hole in my reading for a long time and, even now, I've only read the first though the others are in the Pile. I've read many of his others, though, and loved the Pellucidar books. The Venus books and stuff like the Moon Maid/Men and the kind of Ice Age books (I forget exactly) were all fun adventures but the Pellucidar books had some kind of magic to them. I think the central sun and the idea of it being right here under our feet, impossible as it was, was just enchanting and I think Burroughs felt it, too, as they seemed extra-adventurous, somehow, and he even took Tarzan into it in Tarzan at the Earth's Core. (Is that his only crossover or am I forgetting something?)
In terms of influences, Burroughs himself was influenced by the vast ocean of pre-genre adventure fiction and weird stories. In terms of descendents, I'm reading a Leigh Brackett right now and the color and adventure and strong silent types definitely show the influence and, of course, she and Bradbury have a lot in common in terms of threads of each of their writings (Brackett having other hard-boiled detective interests and whatnot and Bradbury having other soft horror interests, etc., but the planetary romance is common.) The whole magazine of Planet Stories could have been called Edgar Rice Burroughs' Science Fiction Magazine. I think C.L. Moore was probably influenced. Heinlein obviously was, though he usually went in a completely different direction with most strands. But there's still the "honorable valorous adventure" streak even in him.