I always liked Troop's covers of "All I Do Is Think of You" and "Sweet November". Sinead O'Connor's "Nothing Compares 2 U", Chaka Khan's "I Feel For You", Black Crowes' "Hard to Handle", Omar Chandler's "This Must Be Heaven", Ki-Ci's "If You Think You're Lonely Now", LTD's "Love Ballad" (well, I'm not sure if they were the original, George Benson, or someone else), Whitney Houston's "The Greatest Love of All", Aaliyah's "At Your Best (Remix)", most of the Luther and Isley Brothers covers
Thought of some more (not all of these were better than the originals, but many were as good):
En Vogue-"Giving Something He Can Feel"
H-Town-"A Thin Line Between Love and Hate"
Jagged Edge-"All Out of Love"
Mel'issa Morgan-"Do Me Baby"
Jesse and Trina-"Where Is the Love"
After Seven-"Sarah Smile"
Prince-"I Can't Make You Love Me"
Gladys Knight-"I Heard It Through the Grapevine"
Keith Sweat-"Just a Touch"
Prophet Jones-"Cry Together"
Pure Soul/O'Jays-"Stairway to Heaven" (Remix)
Xscape-"Am I Dreaming"
Usher/Monica-"Slow Jam"
Silk-"Ebony Eyes"
Al. B. Sure!-"Killin' Me Softly"
Fugees-"Killin' Me Softly"
Lauryn Hill-"Can't Take My Eyes Off of You"
Gerald Levert/Mary J. Blige-"That's the Way I Feel About 'Cha"
Guy-"Yearnin' For Your Love"
D'Angelo-"Heaven Must Be Like This", "Cruisin'"
All4One-"I Swear"
Taral Hicks-"Silly"
Mary J. Blige-"Sweet Thing"
R. Kelly-"Hey Love," "Sadie"
Gerald Albright-"This is the for the lover in you"
Donell Jones-"My Cherie Amor"
Eva Cassidy-"Time after Time", "Fields of Gold"
Tevin Campbell-"Strawberry Letter 23"
Whitney Houston-"I'm Every Woman"
Nas/Lauryn Hill-"If I Ruled the World" (not sure if its a cover)
LL Cool J-"Ain't Nobody" (not sure it its a cover)