Ian Anderson, left, the leader of British rock band Jethro Tull, performs on stage, during the Festival du Bout du Monde, Aug. 12, 2007, in Crozon, western France.

Jethro Tull declined an invitation to play Woodstock in 1969. Singer Ian Anderson explained the decision in a Q&A with SongFacts.com, saying, "The reason I didn't want to play Woodstock is because I asked our manager, Terry Ellis, 'Well, who else is going to be there?' And he listed a large number of groups who were reputedly going to play, and that it was going to be a hippie festival, and I said, 'Will there be lots of naked ladies? And will there be taking drugs and drinking lots of beer, and fooling around in the mud?' Because rain was forecast. And he said, 'Oh, yeah.' So I said, 'Right. I don't want to go.' Because I don't like hippies, and I'm usually rather put off by naked ladies unless the time is right. Well, indeed, unless the money's right."

From left, John Densmore, Robbie Krieger, Ray Manzarek and Jim Morrison.

The Doors could have played Woodstock, but apparently said no. In 1996, Ray Manzerek explained in an official Doors Web chat, "We never played at Woodstock because we were stupid and turned it down. We thought it would be a second class repeat of Montery Pop Festival."

Joni Mitchell performs at the "Stormy Weather 2002" concert at the Wiltern Theatre on Nov. 13, 2002, in Los Angeles.

Joni Mitchell had originally planned to perform, but her manager urged her to cancel so she can instead do an appearance on "The Dick Cavett Show." Her manager was afraid they'd get caught in traffic and miss the TV appearance.

Mitchell would later make up for it by writing the song "Woodstock" based on what her then-boyfriend Graham Nash said about playing the festival. The song, with the lyric "By the time we got to Woodstock, we were half a million strong," became a classic for Crosby, Stills & Nash.

John Lennon and his wife Yoko Ono receive journalists March 25, 1969 in the bedroom of the Hilton hotel suite in Amsterdam, during their honeymoon in Europe.

There are unconfirmed reports that John Lennon was interested in playing Woodstock. One tale says Lennon he considered heading to New York but was in Candada at the time and had a hard time getting back into the United States.

John Paul Jones, Robert Plant, Jimmy Page and John Bonham 0f Led Zeppelin.

Led Zeppelin was asked to play Woodstock, but the band's manager, Peter Grant, turned it down. Robert Plant told Jimmy Fallon in 2010, "Our management thought we would be typecast." Apparently, Grant didn't want Zep to just be another act in a bill of many. During the weekend of Woodstock, Zep played really close by -- at the Asbury Park Convention Hall in New Jersey.

Justin Hayward and John Lodge, right, perform at Radio City Music Hall on Aug. 20, 2009, in New York.

The Moody Blues had planned to perform (the band was even on the original poster), but decided to pull out after being booked for a gig in Paris that same weekend.

Peter Cetera performs at the 41st annual Songwriters Hall of Fame at The New York Marriott Marquis on June 17, 2010, in New York.

Chicago, which then was still known as Chicago Transit Authority, was originally on the bill for the festival. But the band's promoter, Bill Graham, rescheduled a show at the Fillmore in San Francisco on the same weekend as Woodstock. Santana took Chicago's place.

Singer Peter Cetera told the Spokesman-Review in 2008, "We were sort of peeved at him for pulling that one."

Musician Jeff Beck performs at the MusiCares 2005 Person of the Year Tribute to Brian Wilson at the Palladium on Feb. 11, 2005, in Hollywood, Calif.

The Jeff Beck Group was on the schedule, but never made it to Woodstock. Beck decided to disband the group the night before they were scheduled to take the stage.

"I deliberately broke the group up before Woodstock," Beck was quoted as saying in Annette Carson's Jeff Beck biography. "I didn't want it to be preserved."

Roger McGuinn performs onstage at day 1 of the 2013 Stagecoach California's Country Music Festival at The Empire Polo Field on April 26, 2013, in Indio, Calif.

Organizers asked The Byrds to play Woodstock, but the band members reportedly declined because they didn't think it was going to be that influential of a music event. Plus, there were supposed concerns over money as it was reportedly unclear how much bands would get paid.

Members of Iron Butterfly, from left, Erik Brann, Ron Bushy, Lee Dorman, and Doug Ingle. Dorman on April 9, 1969.

Iron Butterfly was on the bill for the festival, but didn't make because the members got stuck at the airport.

The cover of Procol Harum's 1967 debut album.

Procol Harum was invited to play, but declined because Woodstock fell at the end of a long tour for the band behind the classic "A Whiter Shade of Pale." It was also around the same time guitarist Robin Trower was expecting his child to be born.

Arthur Lee arrives at the "The Mojo Honours List Music Awards" at Banqueting House, Whitehall on June 22, 2004, in London.

Arthur Lee and Love -- known for the 1967 album "Forever Changes -- were invited perform but said no. According to reports, there was "inner turmoil" within the band at the time.

Singer Paul Rodgers attends the Classic Rock Roll of Honour Awards at the Park Lane Hotel on Nov. 2, 2009, in London.

Free, known for the hit "All Right Now," was also reportedly asked to play. But singer Paul Rodgers and the band turned down the invite.

By: Lauren Moraski

Photos: Woodstock's artists 45 years later