Okay, but having your nurse puree it and feed it to you intravenously doesn’t count. You’ll have to gum it.
I’d second several people mentioned before (especially Costello and Porter), but I think I’d rather be the first to mention Stephin Merritt (of the Magnetic Fields and the 6ths, among other groups) and Stew (of the Negro Problem and his own solo career). Good stuff.
Hmpf…what kind of list doesn’t include Willie Nelson?
Shame shame shame.
The late, great Joe Strummer.
I second Neil Peart.
Dave Davies is no slouch himself! 
Lennon & McCartney
Bob Dylan
Anybody mention Neil Young yet?
Elvis Costello would be my choice.
Has Mark Knopfler been mentioned?
And hey, some props to Eddie Vedder.
From the world of country music, Hank Williams, Sr. deserves a mention, as do Merle Haggard and Dwight Yoakam.
Amens to:
Paul Simon
Bob Dylan
Bruce Springsteen
Joe Strummer
Shane Macgowan
I third or fourth, whichever it is, Cole Porter.
And an underrated rock songwriter who never seems to be mentioned on these lists: John Hiatt. Sure, he’ll occasionally dip from a familiar well (rivers, rain, and trains show up a lot), but how can you not love this?
A lot of great names already. I have to add one of my favorites: Donald Fagan of Steely Dan.
Lennon and McCartney, no question.
He wrote the music, not the lyrics. You’re thinking of Yip Harburg or Johnny Mercer (Arlen’s most frequent lyricists).
No one has mentioned Beck.
Pete Townsend
Again, maybe not the best … but I consider Nick Cave in the same league as Tom Waits and Shane MacGowan.
Ira Gershwin
Cole Porter
Stephen Sondheim
and just to add another name (because all of the ones I would have written are already written) Howard Ashman was on his way…
I think there’s a reason for that…
Bob Dylan / Townes Van Zandt
(considerable gap)
Shane MacGowan
Tom Waits
Bruce Springsteen
Johnny Cash
Nick Cave
Leonard Cohen
Guy Clark
Steve Earle
I feel compelled to mention Sting. He’s had some incredible lyrics in some of his songs.
I’m not prepared to make judgements like “the best,” but I think Robert Smith deserves a mention. I just like the way he plays with words. One of my favorites:
I don’t know if I’d say Liz Phair is the greatest lyricist, but she has a way of putting things together that’s very honest.
“I don’t know if I could fly a plane
Well enough to tailspin out your name
Or high enough to lose control completely
Honey, I’m thinking maybe”
(from “Shatter”)
Also, she’s the only one I can think of that hasn’t been listed already. But I’ll cheerfully second Elvis Costello and Robert Smith.