This covers the 1964-1966 period, until the group broke up and Burdon recorded as ’Eric Burdon and the Animals’

Boom Boom (Hooker): John Lee Hooker [‘62, Vee Jay 438]
Talkin’ Bout You (Charles): Ray Charles [‘58, Atlantic 1172]
Dimples (Hooker): John Lee Hooker [‘56, Vee Jay 205]
Baby Let Me Take You Home (Russell, Farrell): a blues tune from the ‘30s with many variations, including Bob Dylan‘s “Baby Let Me Follow You Down“ (see below); this version may be based on ‘Baby Let Me Hold Your Hand’ for Hoagy Lands & the Mustangs [‘64, Atlantic 2217], produced by Bert Burns. *
Gonna Send You Back to Walker (Matthews, Hammond): ‘Gonna Send You Back to Georgia’ by Timmy Shaw [‘64, Wand 146]
Baby What’s Wrong ( Reed): Jimmy Reed [‘62, Vee Jay 425]
The House of the Rising Sun (trad., arr. Price): a country song from the ‘30s which became a much-recorded folk standard. This version is said to be based on Josh White’s [‘56, ABC Paramount LP 124 The Josh White Stories]; Bob Dylan’s [‘62, Bob Dylan, Columbia CK8579] may be another source. *
I’m Mad Again (Hooker): John Lee Hooker [‘61, Vee Jay 379]
The Right Time (Herman): Ray Charles [‘59, Atlantic 2010] *
Around and Around (Berry): Chuck Berry [‘58, Chess 1691]
Bury My Body (trad., arr. Price): Josh White [’56 or ‘57, Josh (Sings Blues) aka Ballads and Blues Elektra EKL-114] and Lonnie Donegan [‘56, U.K. Decca FJ 10695]
She Said Yeah (Jackson, Christy): Larry Williams [‘59, Specialty 658]
The Girl Can’t Help It (Troup): Little Richard [‘56, Specialty 591]
I’ve Been Around (Domino): Fats Domino [‘59, Imperial 5629]
Memphis, Tennessee (Berry): Chuck Berry [‘59, Chess 1729]
Don’t Let Me Be Misunderstood (Benjamin, Marcus, Caldwell): Nina Simone [‘64, Philips 40232]
Roadrunner (McDaniels): Bo Diddley [‘60, Checker 942]
Hallelujah I Love You So (Charles): Ray Charles [‘56, Atlantic 1096]
Don’t Want Much (Gordon): ‘Just a Little Bit’ by Rosco Gordon [‘60, Vee Jay 332] *
I Believe To My Soul (Charles): Ray Charles [‘59, Atlantic 2043]
Let the Good Times Roll (Lee): Shirley & Lee [‘56, Aladdin 3325]
Mess Around (Nugetre): Ray Charles [‘53, Atlantic 999]
How You’ve Changed (Berry): Chuck Berry [‘58, One Dozen Berrys Chess LP 1432]
I Ain’t Got You (Arnold): Jimmy Reed [rec. ‘55, rel. ‘60, Found Love Vee Jay LP-1022]; originally Billy Boy Arnold [’55, Vee Jay 171]
Roberta (Smith, Vincent): Frankie Ford [‘59, Ace 554], with a new vocal substituting for Bobby Marchan’s on ‘Loberta’ by Huey ‘Piano’ Smith & the Clowns [‘59, not released at the time]. It is based on ‘I Ain’t Mad at You (You Ain’t Mad at Me)’ (Basie, Green, Ebbins) in 1947 by Count Basie [Victor 20-2314]. Rypens lists the first version as a 1947 RCA recording by Bobby Merrill; the only Merrill version Lord lists is from 1960 [Bargain 5002], but a non-jazz version may exist.
Bright Lights, Big City (Reed): Jimmy Reed [‘61, Vee Jay 398]
Worried Life Blues (Merriweather): Chuck Berry [‘60, Rockin’ at the Hops Chess LP-1448], originally Big Maceo Merriweather [‘41, Bluebird 8827]. The song actually originated as ‘Someday Baby Blues’ by Sleepy John Estes [‘35, Champion 50038], and is a much-recorded blues under various names, such as ‘Trouble Blues’ by Charles Brown [‘49, Aladdin 3024] and ‘Trouble No More’ by Muddy Waters [‘56, Chess 1612].
Bring It On Home to Me (Cooke): Sam Cooke [‘62, RCA 8036]
We’ve Gotta Get Out of This Place (Mann, Weil): there is a demo by writer Barry Mann.
One Monkey Don’t Stop No Show (Tex): Joe Tex [‘65, Dial 4011]
Maudie (Hooker): John Lee Hooker [‘59, Vee Jay 308]
Outcast (Campbell, Johnson): Eddie & Ernie [‘65, Eastern 608] (these are the writers)
Sweet Little Sixteen (Berry): Chuck Berry [‘58, Chess 1683]
Gin House Blues (Troy, Henderson): Nina Simone [‘61, Colpix 608], previously by Bessie Smith [‘26, Columbia 14158] - but misattributed on Simone’s album - actually ‘Me and My Gin’ written by Harry Burke (James C. Johnson?), recorded in 1928 by Bessie Smith. She also recorded in 1926 the actual song ‘Gin House Blues’ by Henderson and Troy.
Squeeze Her - Tease Her (Tucker, Wilson): Jackie Wilson [‘64, Brunswick 55269]
What Am I Living For (Jay, Harris): Chuck Willis [‘58, Atlantic 1179]
I Put a Spell On You (Hawkins): Nina Simone [‘65, Philips 40296], originally Screamin’ Jay Hawkins [‘56, Okeh 7072] *
That’s All I Am To You (Blackwell, Scott): Ray Charles [‘65, ABC-Paramount 10720]
Inside Looking Out (A. & J. Lomax, Burdon, Chandler): tune is based on ‘Rosie’, recorded by John & Alan Lomax for the Library of Congress in 1936, performed by Dobie Red & Group. The Lomaxes also recorded it in 1947-48, performed by CB, released in 1957 [Negro Prison Songs Tradition 1020].
Help Me Girl (English, Weiss): the Outsiders [‘66, Capitol 5759]
See See Rider (trad., arr. Rowberry): a new arrangement of the 1924 Ma Rainey blues *
I Just Wanna Make Love to You (Dixon): Muddy Waters [‘54, Chess 1571]
Big Boss Man (Smith, Dixon): Jimmy Reed [‘61, Vee Jay 380]
Pretty Thing (McDaniel): Bo Diddley [‘55, Checker 827]
Shake (Cooke): Sam Cooke [‘65, RCA 8486]
The Other Side of This Life (Neil): Fred Neil [‘65, Bleecker & MacDougal Elektra 7293]
Rock Me Baby (King, Josea): B.B. King [‘64, Kent 393], from earlier sources *
Lucille (Penniman, Collins): Little Richard [‘57, Specialty 598]
Smoke Stack Lightning (Burnett): Howlin’ Wolf [‘56, Chess 1618]
Hey Gyp (Donovan): Donovan [‘65, UK Pye 7N 15984], a re-working of ‘Can I Do It For You’ by Memphis Minnie & Kansas Joe [‘30, Vocalion 1523]; it has also been redone as ‘Chevrolet’
Hit the Road, Jack (Mayfield): Ray Charles [‘61, ABC-Paramount 10244]
Louisiana Blues (Muddy Waters): Muddy Waters [‘51, Chess 1441]
Going Down Slow (Oden): St. Louis Jimmy (Oden) [‘41, Bluebird B8889], a much-recorded blues classic
Unknown sources:
Blue Feeling (Henshaw): this is not the Chuck Berry blues instrumental of the same name.
I’m In Love Again (* Domino, Bartholomew): although the title and credits suggest the Fats Domino hit, this is an entirely different song of unknown origin.
The Story of Bo Diddley **(Burdon, McDaniel): Bo Diddley has a song of the same name, but it is different both lyrically and musically. This song is an Eric Burdon recitation over a Bo Diddley-inspired beat.