It's worth noting that the "crossover" events like the Vanishing Tower (not the Dark Tower - that's Stephen King), show up in the respective series of all the Champions involved, where you get to see it from the perspective of the champion who's book it is.
Note - Bane of the Black Sword has a little short story at the end which is a personal favorite of mine for reasons that will become obvious.
Hawkmoon is excellent. Just wait till you get to the end of the third book and the climatic battle. I guarentee it will blow your mind what happens... Though personally, I would avoid the second Hawkmoon series - Castle Brass. It left me feeling gyped, since it essentially negated the end of the original trilogy.
Both Corum series are excellent and highly recommended. Not to mention that you'll find out where the inspiration for the Hand and Eye of Vecna came from.
"The Warhound and the World's Pain" gets another nod from me as well. A suprisingly upbeat and hopeful ending for a Moorecock book.
Personally, I can't really think of another series or writer who has anything really like Moorcock's stuff. Elric in particular is probably the most "anti-heroic" (ie. Conan style) character I've ever seen and certainly the most tortured and out of place one I've read about.
The Song of Fire and Ice, is a very gritty, very realistic fantasy series in which no convention or character is safe. You might want to give that a try.
Fritz Lieber's - Fafhrid and The Grey Mouser books have some of the all time classic fantasy characters and the duo are the architypical rogues. Highly recommended.
The Black Company books by Glen Cook are some of my all time favorites. The main characters go to work for the Evil Sorceress who's just been freed from her centuries long imprisonment. A really terrific cast of characters and plots.
That's all I can really think of for the moment. There really hasn't been that much in the way of really great fantasy. Personally, I've pretty much stopped reading it in favor of SF.
Here's a bibliography of Moorcock books I got off a web site
http://www.multiverse.org/
John Daker novels
The Eternal Champion
The Silver Warriors (Phoenix in Obsidian)
The Swords of Heaven, The Flowers of Hell [graphic novel, with Howard V. Chaykin]
The Dragon in the Sword [cross-listed here and the Von Bek section]
Elric novels
The Elric Saga
Elric of Melniboné (The Dreaming City)
The Fortress of the Pearl
The Sailor on the Seas of Fate [contains a considerably revised version of The Jade Man's Eyes as the final "book"]
The Weird of the White Wolf [linked narrative collection]
The Vanishing Tower (The Sleeping Sorceress)
The Revenge of the Rose
The Bane of the Black Sword [linked narrative collection]
Stormbringer
Other
Elric at the End of Time [published as collection of short stories, only some of which have a connection to the Elric Saga, and also as just the novella, illustrated by Rodney Matthews]
The Singing Citadel [linked narrative collection, only some have a connection to the Elric Saga]
The Stealer of Souls (The Stealer of Souls and Other Stories) [linked narrative collection]
The Jade Man's Eyes [chapbook]
Elric: The Return to Melniboné [short graphic novel, drawn by Philippe Druillet with text by Michael Moorcock]
Hawkmoon novels
Hawkmoon (The History of the Runestaff)
The Jewel in the Skull
The Mad God's Amulet (Sorcerer's Amulet)
The Sword of the Dawn (Sword of the Dawn)
The Runestaff (The Secret of the Runestaff)
The Chronicles of Castle Brass (Count Brass)
Count Brass
The Champion of Garathorm
The Quest for Tanelorn
Corum novels
Corum: The Coming of Chaos (The Swords Trilogy) (The Swords of Corum) (Corum)
The Knight of the Swords
The Queen of the Swords
The King of the Swords
The Prince with the Silver Hand (The Chronicles of Corum)
The Bull and the Spear
The Oak and the Ram
The Sword and the Stallion
Cornelius novels
The Cornelius Chronicles (The Cornelius Quartet)
The Final Programme
A Cure for Cancer
The English Assassin
The Condition of Muzak
A Cornelius Calendar
The Adventures of Una Persson and Catherine Cornelius in the Twentieth Century
The Entropy Tango
The Great Rock 'n' Roll Swindle (Gold Diggers of 1977) [chapbook]
Other
The Lives and Times of Jerry Cornelius [linked narrative collection]
The Nature of the Catastrophe [collection by Michael Moorcock and others, edited by Michael Moorcock and Langdon Jones, cross-listed here and the Editor section]
The New Nature of the Catastrophe [collection by Michael Moorcock and others, edited by Michael Moorcock and Langdon Jones, a massive expansion (with exclusions) of The Nature of the Catasrophe, cross-listed here and the Editor section, and the Omnibus Editions page]
Michael Kane novels [originally as Edward P. Bradbury]
City of the Beast (The City of the Beast) (Warriors of Mars)
Lord of the Spiders (The Lord of the Spiders) (Blades of Mars)
Masters of the Pit (The Masters of the Pit) (Barbarians of Mars)
Oswald Bastable novels
The Warlord of the Air
The Land Leviathan
The Steel Tsar
Dancers at the End of Time
Dancers at the End of Time
An Alien Heat
The Hollow Lands
The End of All Songs
Other
Legends from the End of Time [linked narrative collection]
A Messiah at the End of Time (The Transformation of Miss Mavis Ming) (Constant Fire)
Colonel Pyat novels
Byzantium Endures
The Laughter of Carthage
Jerusalem Commands
The Vengeance of Rome [not yet published]
Von Bek novels
The War Hound and the World's Pain
The City in the Autumn Stars
The Dragon in the Sword [cross-listed here and the John Daker section]