Whitney Houston - I Will Always Love You (original by Dolly Parton)

Birdy - Skinny Love (original by Bon Iver)

Other songs that you know??

Mariah Carey's "Without You"

Mariah Carey's last global song "Without You" aka "Ken Lee".

Mariah Carey's global song "Without You", and it's not the last global hit she has even though someone else claims so

Jeff Buckley's version of Hallelujah. Ten times better than that raspy original.

Roar

The best example I can think of is Natalie Imbruglia's Torn.

Guess the original

Bette Davis Eyes - Kim Carnes
Without You - Mariah Carey
Hallelujah - Jeff Buckley
Hallelujah - Alexandra Burke ()
If You Asked Me To - Celine Dion ()
Tutti Frutti - Pat Boone ()
Hound Dog - Elvis Presley

American Pie

Celine's All By Myself

Last? If anything that is her first global song.

OH nvm. The OP asks for bigger, not better.

Kylie Minogue - On A Night Like This. I think the original belongs to Pandora or Anna Vissi.

Hurt - Johnny Cash

Aaliyah - At Your Best
original by The Isley Brothers