source Some thoughts:
Most are from the 1986 to 1993 time frame. Not really suprised since that most of the music from that time period is frowned upon (by MTV) with exception from a few artists that are either alternative, hardcore rap, Madonna, or Michael Jackson. Funny to see Pearl Jam as one of the nominations for one of the worst since MTV tends to kiss-up to them and even ranked "Jeremy" as one of their 100 Greatest Music Videos Ever Made...also ranked in 1999.
Plus classics from Bon Jovi, Robert Palmer, B-52's, Whitesnake, Sir Mix-a-Lot to name a few...
The 25 were chosen out of a list of 50.
Journey & Billy Squier, which were on the official list weren't even listed as one of the choices.
Marky Mark, New Kids, Hootie & The Blowfish, U2, Marilyn Manson, & Culture Club were on the Top 25.
Granted that things could've slightly changed, but some were already in the middle or towards the Top 10.
Deb still at 10, ugh!!!
The producers might've taken Marilyn Manson out due to fear of tasteless jokes about the Columbine tragedy that happened around the time. Though doesn't explain about the rest.
Hootie & The Blowfish's popularity was already faded and despite U2 was still kissed up by MTV, "Discotheque" isn't even considered their best. As for New Kids, maybe because two of the members were releasing albums...
Vanilla Ice was at 40 
Though he was probably already asked to be on the show beforehand. Strongly agree that it's worthy of being on the Top 10.
Then again, the list was from MTV... 
When the special aired, I started disliking the channel more since I actually like a handful of the songs/videos and wasn't into majority of the "music" on TRL.
Ranking from May 8th, 1999, which the special aired on May 9th. Voted by "MTV viewers"50. Stay - Lisa Loeb
49. Baby Got Back - Sir Mix-A-Lot
48. B!tch - Meredith Brooks
47. Believe - Cher
46. Mickey - Toni Basil
45. Love Shack - B-52s
44. Jeremy - Pearl Jam
43. The Sign - Ace of Base
42. Jump - Kris Kross
41. Livin' On A Prayer - Bon Jovi
40. Ice Ice Baby - Vanilla Ice
39. Here I Go Again - Whitesnake
38. Everything I Do - Bryan Adams
37. Addicted To Love - Robert Palmer
36. Wannabe - Spice Girls
35. Pump Up The Jam - Technotronic
34. MMMBop - Hanson
33. Every Rose Has Its Thorn - Poison
32. Da Dip - Freak Nasty
31. I'm Too Sexy - Right Said Fred
30. Rush Rush (Short) - Paula Abdul
29. I'm Gonna Be (500 Miles) - Proclaimers
28. I Would Do Anything For Love - Meat Loaf
27. Two Princes - Spin Doctors
26. 2 Legit 2 Quit - Hammer
25. Good Vibrations - Marky Mark
24. You Got It (The Right Stuff) - New Kids On The Block
23. Hold On - Wilson Phillips
22. Hold My Hand - Hootie and The Blowfish
21. What's Up - 4 Non Blondes
20. Informer - Snow
19. Without You - Motley Crue
18. Discotheque - U2
17. Tubthumping - Chumbawamba
16. Heaven - Warrant
15. Barbie Girl - Aqua
14. MMM MMM MMM MMM - Crash Test Dummies
13. Sweet Dreams - Marilyn Manson
12. Do You Really Want To Hurt Me - Culture Club
11. Wake Me Up - Wham!
10. Electric Youth - Debbie Gibson
9. Seventeen - Winger
8. Rico Suave - Gerardo
7. Maneater - Hall & Oates
6. Girl You Know It's True - Milli Vanilli
5. After The Rain - Nelson
4. Whatzupwitu - Eddie Murphy
3. Macarena - Los Del Rio
2. OWWW! - Chunky A.
1. Heartbeat - Don Johnson
MTV 25 Lame (1999)25. Spin Doctors "Two Princes" (1993)
24. Hammer "2 Legit 2 Quit" (1991)
23. Wilson Phillips "Hold On" (1990)
22. Chumbawamba "Tubthumping" (1997)
21. Billy Squier "Rock Me Tonight" (1984)
20. 4 Non Blondes "What's Up" (1993)
19. Motley Crue "Without You" (1990)
18. Snow "Informer" (1993)
17. Paula Abdul "Rush Rush" (1991)
16. Warrant "Heaven" (1989)
15. Crash Test Dummies "Mmm Mmm Mmm Mmm" (1994)
14. Aqua "Barbie Girl" (1997)
13. Journey "Separate Ways" (1983)
12. Winger "Seventeen" (1989)
11. Wham! "Wake Me Up Before You Go Go" (1984)
10. Debbie Gibson "Electric Youth” (1989)
9. Vanilla Ice "Ice, Ice, Baby" (1990)
8. Milli Vanilli "Girl You Know It's True" (1989)
7. Gerardo "Rico Suave" (1991)
6. Hall & Oates "Maneater" (1982)
5. Los Del Rio "Macarena" (1996)
4. Nelson "After The Rain" (1990)
3. Eddie Murphy featuring Michael Jackson "Whazupwitu" (1993)
2. Chunky A "Owww!" (1989)
1. Don Johnson "Heartbeat" (1986)
