Singer Darlene Love, whose voice cut through Phil Spector's "Wall of Sound," called her induction into the Hall her best 70th birthday present.
Pianist Leon Russell also was to be inducted at a black-tie dinner at The Waldorf-Astoria hotel in Manhattan. A tape of the ceremony is to air March 20 on Fuse.
Dr. John said he felt "like I'm blessed to be singing, to be breathing."
He was inducted by singer John Legend, who recalled meeting him at a benefit for Hurricane Katrina relief. Legend said the new Hall of Fame member has been a leading global ambassador for New Orleans and its special musical gumbo.
"He has never stopped flying the flag of funk," Legend said. "Tonight, he is definitely in the right place at the right time."
That was a reference to one of Dr. John's best-known songs, "Right Place, Wrong Time," with Allen Toussaint and the Meters.
Love fought back tears in her acceptance speech, saying she had faith that the gift God gave her would sustain her for the rest of her life.
She was inducted with a comic ramble by Bette Midler, who said she was a goner when she first heard Love's voice on a transistor radio.
"Listening to her songs, you had to dance, you had to move, you had to keep looking for that rebel boy," Midler said.
Love lent her powerful voice to several of Spector's hits, in acts such as the Crystals and Bob B. Soxx and the Blue Jeans. Her "Christmas (Baby Please Come Home)" is a holiday standard: She sang on U2's cover and performs it every December on David Letterman's show.
The Brooklyn-born Diamond wrote pop-rock hits for himself ("Solitary Man") and others (The Monkees' "I'm a Believer"). Presidential daughter Caroline Kennedy was the inspiration for "Sweet Caroline," now a Boston Red Sox anthem. Diamond settled into a comfortable career as a middle-of-the-road concert favorite, although he made some challenging recordings in recent years with producer Rick Rubin.
He said before the ceremony that he had flown in from a concert tour in Australia for his induction and was flying back when it was done.
Alice Cooper is the stage name for singer Vincent Furnier and his band, known for 1970s era hard rock songs "Eighteen," "No More Mr. Nice Guy" and "School's Out." Their concerts were steeped in horror movie theatrics, and singer Rob Zombie said Monday they had invented the rock show.
Cooper wore a blood-splattered shirt and a boa constrictor to the induction. He said, "We've always been a hard rock band. We just wanted to decorate it a little differently."
Songwriter Waits is well-versed in blues, poetry and ballads, with songs rough and romantic. Several of his Hall of Fame predecessors have recorded his work, including Bruce Springsteen ("Jersey Girl"), the Ramones ("I Don't Want to Grow Up"), Rod Stewart ("Downtown Train") and Johnny Cash ("Down There By the Train"). Another California-based songwriter, Neil Young, was to pay tribute to Waits on Monday.
Russell's long hair and beard gave him a distinctive look, but it's the piano player's songs - particularly "Delta Lady" and "A Song for You" - that made him memorable. His career has recently been revived through a collaboration with Elton John, who was to induct him.
Elektra Records founder Jac Holzman and Specialty Records founder Art Rupe were to be inducted in the non-performer category.
The rock hall has slightly shifted its format this year, doing the inductions first then gathering artists for performances. In past years, the performances were interspersed throughout the night.