1 In The Wee Small Hours by Frank Sinatra (Capitol) 1955

Actually, the very first 'concept' album. The idea being you put this record on after dinner and by the last song you are exactly where you want to be. Sinatra said that he's certain most baby boomers were conceived with this as the soundtrack.

2 Solo Monk by Thelonious Monk (Columbia) 1964

Monk said 'There is no wrong note, it has to do with how you resolve it'. He almost sounded like a kid taking piano lessons. I could relate to that when I first started playing the piano, because he was decomposing the music while he was playing it. It was like demystifying the sound, because there is a certain veneer to jazz and to any music, after a while it gets traffic rules, and the music takes a backseat to the rules. It's like aerial photography, telling you that this is how we do it. That happens in folk music too. Try playing with a bluegrass group and introducing new ideas. Forget about it. They look at you like you're a communist. On Solo Monk, he appears to be composing as he plays, extending intervals, voicing chords with impossible clusters of notes. 'I Should Care' kills me, a communion wine with a twist. Stride, church, jump rope, Bartok, melodies scratched into the plaster with a knife. A bold iconoclast. Solo Monk lets you not only see these melodies without clothes, but without skin. This is astronaut music from Bedlam.

3 Trout Mask Replica by Captain Beefheart (Straight) 1969

The roughest diamond in the mine, his musical inventions are made of bone and mud. Enter the strange matrix of his mind and lose yours. This is indispensable for the serious listener. An expedition into the centre of the earth, this is the high jump record that'll never be beat, it's a merlot reduction sauce. He takes da bait. Dante doing the buck and wing at a Skip James suku jump. Drink once and thirst no more.

4 Exile On Main St. by Rolling Stones (Rolling Stones Records) 1972

'I Just Want To See His Face' - that song had a big impact on me, particularly learning how to sing in that high falsetto, the way Jagger does. When he sings like a girl, I go crazy. I said, 'I've got to learn how to do that.' I couldn't really do it until I stopped smoking. That's when it started getting easier to do. [Waits's own] 'Shore Leave' has that, 'All Stripped Down', 'Temptation'. Nobody does it like Mick Jagger; nobody does it like Prince. But this is just a tree of life. This record is the watering hole. Keith Richards plays his ass off. This has the Checkerboard Lounge all over it.

5 The Sinking of the Titanic by Gavin Bryars (Point Music) 1975

This is difficult to find, have you heard this? It's a musical impression of the sinking of the Titanic. You hear a small chamber orchestra playing in the background, and then slowly it starts to go under water, while they play. It also has 'Jesus Blood' on it. I did a version of that with Gavin Bryars. I first heard it on my wife's birthday, at about two in the morning in the kitchen, and I taped it. For a long time I just had a little crummy cassette of this song, didn't know where it came from, it was on one of those Pacifica radio stations where you can play anything you want. This is really an interesting evening's music.

6 The Basement Tapes by Bob Dylan (Columbia) 1975

With Dylan, so much has been said about him, it's difficult so say anything about him that hasn't already been said, and say it better. Suffice it to say Dylan is a planet to be explored. For a songwriter, Dylan is as essential as a hammer and nails and a saw are to a carpenter. I like my music with the rinds and the seeds and pulp left in - so the bootlegs I obtained in the Sixties and Seventies, where the noise and grit of the tapes became inseparable from the music, are essential to me. His journey as a songwriter is the stuff of myth, because he lives within the ether of the songs. Hail, hail The Basement Tapes. I heard most of these songs on bootlegs first. There is a joy and an abandon to this record; it's also a history lesson.

7 Lounge Lizards by Lounge Lizards (EG) 1980

They used to accuse John Lurie of doing fake jazz - a lot of posture, a lot of volume. When I first heard it, it was so loud, I wanted to go outside and listen through the door, and it was jazz. And that was an unusual thing, in New York, to go to a club and hear jazz that loud, at the same volume people were listening to punk rock. Get the first record, The Lounge Lizards. You know, John's one of those people, if you walk into a field with him, he'll pick up an old pipe and start to play it, and get a really good sound out of it. He's very musical, works with the best musicians, but never go fishing with him. He's a great arranger and composer with an odd sense of humour.

8 Rum Sodomy and the Lash by The Pogues (Stiff) 1985

Sometimes when things are real flat, you want to hear something flat, other times you just want to project onto it, something more like.... you might want to hear the Pogues. Because they love the West. They love all those old movies. The thing about Ireland, the idea that you can get into a car and point it towards California and drive it for the next five days is like Euphoria, because in Ireland you just keep going around in circles, those tiny little roads. 'Dirty Old Town', 'The Old Main Drag'. Shane has the gift. I believe him. He knows how to tell a story. They are a roaring, stumbling band. These are the dead end kids for real. Shane's voice conveys so much. They play like soldiers on leave. The songs are epic. It's whimsical and blasphemous, seasick and sacrilegious, wear it out and then get another one.

9 I'm Your Man by Leonard Cohen (Columbia) 1988

Euro, klezmer, chansons, apocalyptic, revelations, with that mellifluous voice. A shipwrecked Aznovar, washed up on shore. Important songs, meditative, authoritative, and Leonard is a poet, an Extra Large one.

10 The Specialty Sessions by Little Richard (Specialty Records) 1989

The steam and chug of 'Lucille' alone pointed a finger that showed the way. The equipment wasn't meant to be treated this way. The needle is still in the red.

11 Startime by James Brown (Polydor) 1991

I first saw James Brown in 1962 at an outdoor theatre in San Diego and it was indescribable... it was like putting a finger in a light socket. He did the whole thing with the cape. He did 'Please Please Please'. It was such a spectacle. It had all the pageantry of the Catholic Church. It was really like seeing mass at St. Patrick's Cathedral on Christmas and you couldn't ignore the impact of it in your life. You'd been changed, your life is changed now. And everybody wanted to step down, step forward, take communion, take sacrament, they wanted to get close to the stage and be anointed with his sweat, his cold sweat.

12 Bohemian-Moravian Bands by Texas-Czech (Folk Lyric) 1993

I love these Czech-Bavarian bands that landed in Texas of all places. The seminal river for mariachi came from that migration to that part of the United States, bringing the accordion over, just like the drum and fife music of post slavery, they picked up the revolutionary war instruments and played blues on them. This music is both sour and bitter, and picante, and floating above itself like steam over the kettle. There's a piece called the 'Circling Pigeons Waltz', it's the most beautiful thing - kind of sour, like a wheel about to go off the road all the time. It's the most lilting little waltz. It's accordion, soprano sax, clarinet, bass, banjo and percussion.

13 The Yellow Shark by Frank Zappa (Barking Pumpkin) 1993

It is his last major work. The ensemble is awe-inspiring. It is a rich pageant of texture in colour. It's the clarity of his perfect madness, and mastery. Frank governs with Elmore James on his left and Stravinsky on his right. Frank reigns and rules with the strangest tools.

14 Passion for Opera Aria (EMI Classics) 1994

I heard 'Nessun Dorma' in the kitchen at Coppola's with Raul Julia one night, and it changed my life, that particular Aria. I had never heard it. He asked me if I had ever heard it, and I said no, and he was like, as if I said I've never had spaghetti and meatballs - 'Oh My God, Oh My God!' - and he grabbed me and he brought me into the jukebox (there was a jukebox in the kitchen) and he put that on and he just kind of left me there. It was like giving a cigar to a five-year old. I turned blue, and I cried.

15 Rant in E Minor by Bill Hicks (Rykodisc) 1997

Bill Hicks, blowtorch, excavator, truthsayer and brain specialist, like a reverend waving a gun around. Pay attention to Rant in E Minor, it is a major work, as important as Lenny Bruce's. He will correct your vision. His life was cut short by cancer, though he did leave his tools here. Others will drive on the road he built. Long may his records rant even though he can't.

16 Prison Songs: Murderous Home Alan Lomax Collection (Rounder Select) 1997

Without spirituals and the Baptist Church and the whole African-American experience in this country, I don't know what we would consider music, I don't know what we'd all be drinking from. It's in the water. The impact the whole black experience continues to have on all musicians is immeasurable. Lomax recorded everything, from the sounds of the junkyard to the sound of a cash register in the market... disappearing machinery that we would no longer be hearing. You know, one thing that doesn't change is the sound of kids getting out of school. Record that in 1921, record that now, it's the same sound. The good thing about these is that they're so raw, they're recorded so raw, that it's just like listening to a landscape. It's like listening to a big open field. You hear other things in the background. You hear people talking while they are singing. It's the hair in the gate.

17 Cubanos Postizos by Marc Ribot (Atlantic) 1998

This Atlantic recording shows off one of many of Ribot's incarnations as a prosthetic Cuban. They are hot and Marc dazzles us with his bottomless soul. Shaking and burning like a native.

18 Houndog by Houndog (Sony) 1999

Houndog, the David Hidalgo [Los Lobos] record he did with Mike Halby [Canned Heat]. Now that's a good record to listen to when you drive through Texas. I can't get enough of that. Anything by Latin Playboys, anything by Los Lobos. They are like a fountain. The Colossal Head album killed me. Those guys are so wild, and they've gotten so cubist. They've become like Picasso. They've gone from being purely ethnic and classical, to this strange, indescribable item that they are now. They're worthwhile to listen to under any circumstances. But the sound he got on Houndog, on the electric violin ... the whole record is a dusty road. Dark and burnished and mostly unfurnished. Superb texture and reverb. Lo fi and its highest level. Songs of depth and atmosphere. It ain't nothin' but a...

19 Purple Onion by Les Claypool (Prawn Song) 2002

Les Claypool's sharp and imaginative, contemporary ironic humour and lightning musicianship makes me think of Frank Zappa. 'Dee's Diner' is like a great song your kid makes up in the car on the way to the drive-in. Songs for big kids.

20 The Delivery Man by Elvis Costello (Mercury) 2004

Scalding hot bedlam, monkey to man needle time. I'd hate to be balled out by him, I'd quit first. Grooves wide enough to put your foot in and the bass player is a gorilla of groove. Pete Thomas, still one of the best rock drummers alive. Diatribes and rants with steam and funk. It has locomotion and heat. Steam heat, that is.

· Tom Waits's most recent album, 'Real Gone' is released on Anti

Win Win Win

We have one set of Tom Waits's 20 favourite CDs, courtesy of Fopp, and a signed vinyl copy of his most recent album Real Gone to give away. Plus a signed copy of Real Gone for one runner-up. To be in with a chance to win, go to observermusicmonthly.co.uk or send a postcard marked 'Observer/ Tom Waits' with your name, address and telephone number to Freepost MID 20916 Birmingham B26 3QQ by 4 April 2005. Full terms and conditions online.

To read about a further nine more of Tom Waits's favourite records on The Observer blog.