Old is relative, some of the songs I see here were songs I liked or loved in my teens, 20's and beyond. I'll answer the question for songs made before I was 5 years old.
At Last - Etta James (1960) a fantastic cover of the song from the 1941 musical movie Sun Valley Serenade
Isn't It Loverly - Julie Andrews (1956) from the Broadway cast soundtrack of My Fair Lady
Cast Your Fate To The Wind - Vince Guaraldi (1962) - A wonderful light jazz piano tune
Please take into consideration that if I had considered "old" to be anything below 1990 one of my songs would be Bad Acid by Vomit Launch (1988)
Hey Jude - The Beatles
Isn’t she lovely - Stevie Wonder
Bohemian Rhapsody - QUEEN
Billie Jean - Michael Jackson
Most MJ songs
Most Backstreet boys songs
Break my Stride - Matthew Wilder
Jailhouse Rock - Elvis
The girl is mine - MJ & Paul McCartney
(Sittin' On) The dock of the Bay - Otis Redding
Purple Rain - Prince
When doves cry - Prince
Rocknroll Loveaffair - Prince
In Bangla, There are many, like-
* Eta Ki 2441139? (Is It 2441139?);
*Shadhinotar Mane (Meaning of Freedom);
*Coffee Houser Sei Addata (That Nostalgic Coffee House) & so on..
david bowie - starman
nirvana - smell like teen spirit, come as you are
beatles - hey jude, something
doors - riders on the storm
rolling stones - paint it black
Otis Redding - Sittin on the dock of the bay
Simon and Garfunkel - Sound of Silence
Ralph Mctell - Streets of London
Nina Simone - Feeling Good
Dolly Parton - Jolene
Muddy Waters - Mannish Boy