I don't think anything's really required reading for D&D, but Lovecraft's influence is vast in the realms of both fantasy and horror. I'd say he's one of the most influential authors of the century.
With that said, his writings are somewhat tough to read at times. He has a fairly dense and archaic prose, and his views on race and social class are ... well, representative of his time, I'll say. There's a healthy dose of xenophobia, racism, and elitism thrown in with some otherwise great yarns.
I think reading Lovecraft has improved both my Call of Cthulhu games (of course) and my D&D games. While not everyone will find his work scary, I find it a bit unsettling in a cosmic sort of way. It's not the sort of stuff that keeps me up at night, but there's a strange kind of spookiness to it, IMO.
My favorite stories are The Dunwich Horror, At the Mountains of Madness, and (though I'm probably the only one) the very short and rather creepy Nyarlathotep. I also have a lot of love for both The Shadow out of Time and The Call of Cthulhu itself.
While I wouldn't say it's required, I'd recommend picking up one of the better compilations and reading a story or two. It might not be for you - like I mentioned, the wording is archaic, the science is dated, and there are some kind of uncomfortable cultural assumptions. But if you can look at them as products of a writer who was himself the product of his time, they're pretty remarkable.
-O