Parliament and Funkadelic are definitely classics, the first is funkier and relies more on its horn section while the latter is very Sly inspired rock. Eddie Hazel, the guitar player, is amazing and has a pretty good solo album called "Game, Dames & Guitar Thangs".
From Parliament I would recommend "The Mothership Connection", whilst for Funkadelic I think "Maggot Brain" is a good place to start.
As much as it may pain a lot of people, Prince has done some of the best funk around. My favorite Prince album is "Sign o' the Times", but if you find that to be too pop-oriented for you, you will surely find what you're looking for on other albums such as his Black Album, "The Gold Experience", "O(+> (Love Symbol)", or if you find the time for a little sense of humor, "Dirty Mind".
Also, don't forget to check out all the classic funk-oriented jazzmen. I suppose you know Herbie Hancock's "Headhunters", but he has other good albums. There's also Victor Wooten (talk about slap bass!), maybe Weather Report, and Miles, definitely Miles.
It really depends on what kind of funk you are looking for. If you're looking for more recent stuff, Roy Hargrove's band The RH Factor ("Hard Groove") is quite interesting. If it's classic more r&b/soul stuff your looking for, the list would be huge and would include the likes of Curtis Mayfield, Baby Huey, Sly Stone, Ike & Tina Turner, Wah-Wah Watson. If you're not prejudiced against hip hop, there are some great funky bands like De La Soul, Grandmaster Flash & The Furious Five (only the first album, please!), etc.
Anyway, I hope you will find what you're looking for and, if you have any questions, I would be glad to help as I have been a big funk fan for a while!