WADR - where did you get that list? Louis Armstrong? Too many metal and hard rock bands on that list to be real (sorry, they're never that popular!). Billboard I believe:
1 FAITH, George Michael (Columbia)
2 NEED YOU TONIGHT, INXS (Atlantic)
3 GOT MY MIND SET ON YOU, George Harrison
4 NEVER GONNA GIVE YOU UP, Rick Astley (RCA)
5 SWEET CHILD O' MINE, Guns N' Roses
6 SO EMOTIONAL, Whitney Houston
7 HEAVEN IS A PLACE ON EARTH, Belinda Carlisle (MCA)
8 COULD'VE BEEN, Tiffany (MCA)
9 HANDS TO HEAVEN, Breathe (A&M)
10 ROLL WITH IT, Steve Winwood (Virgin)
11 ONE MORE TRY, George Michael (Columbia)
12 WISHING WELL, Terence Trent D'Arby (Columbia)
13 ANYTHING FOR YOU, Gloria Estefan and the Miami Sound Machine (Epic)
14 THE FLAME, Cheap Trick (Epic)
15 GET OUTTA MY DREAMS, GET INTO MY CAR, Billy Ocean (Jive)
16 SEASONS CHANGE, Expose (Arista)
17 IS THIS LOVE, Whitesnake (Geffen)
18 WILD, WILD WEST, The Escape Club (Atlantic)
19 POUR SOME SUGAR ON ME, Def Leppard (Mercury)
20 I'LL ALWAYS LOVE YOU, Taylor Dayne (Arista)
I provided the link, not sure the veracity of it. Where did you get your list? Google didn't show anything within the first three pages that matches your list, but maybe google is slipping a little.
I thought Louis Armstrong was a bit weird too.