I think that Elvis Costello is widely known to be a music geek, with his 500 albums list. And, Yo La Tengo tend to dig pretty deep on their covers. Which other artists are known as or would you guess are obsessive music geeks?

...Paul Morley...

James Murphy of LCD Soundsystem and DJ Shadow are the first two that come to mind.

IIRC, Thurston Moore (of Sonic Youth) is a big music geek.

Annie is a self-professed music geek. Chromeo too.

Predictable contribution, but still:
Bobby hoary "Must-be-Santa" Dylan has done quite a bit of DJ'ing on the radio, showing off his very wide tastes. He likes to pretend that he only knows stuff from before the 1950's, but the pretense isn't really succesful.

Peter Buck (REM) and Fred Schneider (B-52s) for sure.

And there's Stephin Merritt (Magnetic Fields), who, like Costello, has a list on AM (and a more interesting one at that).

Julian Cope has authored two books on music and runs nifty content about fairly obscure artists on his website. So I would say that qualifies him.

Where can I find Stephin Merritt's list?

Yo La Tengo, as evidenced by their eclectic covers album, Fakebook.

Steven Van Zandt although his range isn't very broad.

Scott Miller of Game Theory/Loud Family... has posted yearly album lists back through early 1960's.

Here's Mr. Merritt's list. He selected one recording from each year of the 20th century.

1900 Tosca (Puccini)
1901 Marie Tempest, soprano: "Les filles de Cadix" (Delibes)
1902 "The Entertainer" (Joplin)
1903 Joseph Joachim, violin: "Hungarian Dance No. 2 in D minor" (Brahms)
1904 "Meet Me in St. Louis, Louis" (Sterling-Mills)
1905 Suite bergamesque (Debussy)
1906 "Love Is Like a Cigarette" (Victor Herbert)
1907 "Pomp and Circumstance" (Elgar)
1908 "I Wonder Who’s Kissing Her Now" (Joe Howard)
1909 "Alexander’s Ragtime Band" (Irving Berlin)
1910 Prometheus (Scriabin)
1911 Posthumous debut of Das Lied von der Erde (Mahler)
1912 "That Shakespearian Rag" (Buck-Ruby-Stamper)
1913 Le sacre du printemps (Stravinsky)
1914 "I’ve a Shooting Box in Scotland" (Cole Porter)
1915 "Play a Simple Melody" (Berlin)
1916 The Planets (Holst)
1917 The Original Dixieland Jazz Band: "(Back Home Again in) Indiana"
1918 "The Real American Folk Song (Is a Rag)" (Gershwins)
1919 Al Jolson: "Swanee"
1920 Musique d’ameublement (Satie)
1921 Fanny Brice: "My Man"
1922 114 Songs (Ives)
1923 Eddie Cantor: "Yes, We Have No Bananas"
1924 Ukulele Ike: "Fascinatin’ Rhythm"
1925 "Manhattan" (Rodgers & Hart)
1926 George Gershwin, piano: "Someone to Watch over Me" (Gershwins)
1927 Showboat (Kern & Hammerstein)
1928 Eddie Cantor: "Makin’ Whoopee"
1929 Maurice Chevalier: "Louise"
1930 "Love for Sale" (Porter)
1931 Gracie Fields: "Sally"
1932 "It Don’t Mean a Thing If It Ain’t Got That Swing" (Duke Ellington, Billy Strayhorn)
1933 Ethel Waters: "Stormy Weather"
1934 Goebel Reeves: "Hobo’s Lullaby"
1935 Top Hat score (Berlin)
1936 Peter and the Wolf (Prokofiev)
1937 "My Funny Valentine" (Rodgers & Hart)
1938 Ella Fitzgerald: "A Tisket, a Tasket"
1939 Glenn Miller: "In the Mood"
1940 Wilf Carter: "You Are My Sunshine"
1941 Billie Holiday: "God Bless the Child"
1942 "Be Careful, It’s My Heart" (Berlin)
1943 Vera Lynn: "I’ll Be Seeing You"
1944 Les Brown and His Orchestra with Doris Day: "Sentimental Journey"
1945 Edith Piaf: "La vie en rose"
1946 Bill Monroe and His Bluegrass Boys: "Blue Moon of Kentucky"
1947 "Be a Clown" (Porter)
1948 Four Last Songs (Richard Strauss)
1949 Vaughn Monroe and His Orchestra: "Riders in the Sky (A Cowboy Legend)"
1950 Patti Page with Jack Rael and Orchestra: "The Tennessee Waltz"
1951 "4’33"," a.k.a. the silent piece (John Cage)
1952 Folkways’ Anthology of American Folk Music
1953 Screamin’ Jay Hawkins: "(She Put the) Wamee (On Me)"
1954 Judy Garland: "The Man That Got Away"
1955 Julie London: "Cry Me a River"
1956 Forbidden Planet score (Bebe and Louis Barron)
1957 Black Orpheus score (Jobim)
1958 The Diamonds: "The Stroll"
1959 Gypsy (Styne-Sondheim), starring Ethel Merman
1960 Psycho score (Bernard Herrmann)
1961 The Paris Sisters: "I Love How You Love Me"
1962 The Tornadoes: "Telstar"
1963 The Ronettes: "Be My Baby"
1964 Dionne Warwick: "Walk on By"
1965 Ellie Greenwich: "You Don’t Know"
1966 The Velvet Underground and Nico
1967 The Jefferson Airplane: Surrealistic Pillow
1968 The United States of America: The United States of America
1969 Serge Gainsbourg and Jane Birkin: "Je T’Aime" (Gainsbourg)
1970 I Am Sitting in a Room (Alvin Lucier)
1971 Joni Mitchell: Blue
1972 Michael Jackson: "Ben"
1973 A Little Night Music (Sondheim)
1974 George McCrae: "Rock Your Baby"
1975 Kraftwerk: Radio-activity
1976 ABBA: "Dancing Queen"
1977 Electric Light Orchestra: Out of the Blue
1978 Blondie: Parallel Lines
1979 Gary Numan: "Cars"
1980 Young Marble Giants: Colossal Youth
1981 The Human League: Dare
1982 Roxy Music: Avalon
1983 New Order: "Blue Monday"
1984 Cocteau Twins: Treasure
1985 Les Rita Mitsuko: "Marcia Baila"
1986 The Jesus and Mary Chain: Psychocandy
1987 MARRS: "Pump Up the Volume"
1988 Marc Almond: Mother Fist and Her Five Daughters
1989 Chris Knox: "Not Given Lightly"
1990 Public Enemy: "911 Is a Joke"
1991 Boyd Rice and Friends: Music, Martinis and Misanthropy
1992 Tom Waits, Bone Machine
1993 Pet Shop Boys: "Dreaming of the Queen"
1994 Saint Etienne: "Like a Motorway"
1995 Pulp: Different Class
1996 Gravikords, Whirlies & Pyrophones, Experimental Musical Instruments
1997 White Town: "Your Woman"
1998 Dancing with the Dead, The Music of Global Death Rites
1999 Fox, Inc.: "Obvious Fake"

The link at AM is broken, but I found it here:
http://1930sblog.blogspot.com/2009/02/stephin-merritts-millenium-music-list.html

I would also add Lucinda Williams, Patterson Hood (Drive by Truckers) and Craig Finn (Hold Steady) based on their eclectic recommendations on Amazon.com.

It looks like Merritt's list is a mix of albums and songs.

Pete Townshend has done a fair bit of entertaining writing about music, and might well qualify as the uber-geek of the 60s (British division).

A question: how would y'all define music geekdom?

I would leave it open for interpretation :)