Quite a lot here, but I'm a bit of a Fifties buff:-
Almost all Elvis songs recorded between 1954 and 1958, but especially "Lawdy Miss Clawdy", "Trying To Get to You" and "Blue Moon"
Most of Chuck Berry's 1950's output
Ditto for Little Richard, Buddy Holly, Jerry Lee Lewis, the Everly Brothers, Eddie Cochran and Fats Domino
"Smoke Gets In Your Eyes" and "My Prayer" by the Platters
"Shake Rattle and Roll" by Big Joe Turner
"Night Time is the Right Time" by Ray Charles
"You Send Me" by Sam Cooke
"Mack The Knife" by Bobby Darin
"Little Bitty Pretty One" by Thurston Harris and the Sharps
"I Only Have Eyes For You" by the Flamingoes
"One Summer Night" by the Danleers
"Ruby Baby" by the Drifters
"Reet Petite" by Jackie Wilson
"Shop Around" by the Miracles
"Where and When" and "I Wonder Why" by Dion and the Belmonts
"Everytime We Say Goodbye" by Ella Fitzgerald
"Move It" by Cliff Richard
"Rock Island Line" by Lonnie Donegan
and load of others that have slipped my mind.