They're a loosely connected canon, sharing concepts, ideas, objects (like the Necronomicon), locations (like Arkham) and characters (like Randolph Carter) between them.
Some things I recommend to get more into the overall Mythos are The Shadow Over Innsmouth, The Dunwich Horror and The Call of Cthulhu. I've also heard good things about At The Mountains of Madness, but haven't read it yet.
Not as closely tied to the Mythos, but a darn good, creepy story is The Colour Out Of Space. And Herbert West - Re-Animator is pretty good too.
If you want to learn more about the Dreamlands, and a bit about Mythos deities like Nodens, Nyarlathotep and Azathoth, read the wonderful Dream-Quest of Unknown Kadath.
Oh, and while not a story by Lovecraft (or even a story at all), maybe also check out Stealing Cthulhu by Graham Walmsley. It's mostly about how to write scenarios for lovecraftian role-playing games, but also has stuff like a lil beastiary and a bibliography.