0:00 - 0:28 - The Big O. First episode.
0:28 ("It's coming") - ???
0:29 - 0:35 - Probably Gundam Wing.
0:35 - Dragon Ball Z. Probably main series. I suspect they're operating on Frieza after his defeat.
0:38 - Superman The Animated Series. I believe this advert predates the Justice League cartoons.
0:42 (and the voiceover that overlaps previous) - Gundam Wing
0:43 - 1:08 - The Big O. Spliced from multiple episodes. The explosion at the end could be from another series.
1:10 - Gundam Wing
1:14 - Superman The Animated Series. Episode collection The World's Finest, a crossover with Batman TAS
1:16 - Dragon Ball Z, probably the film The World's Strongest
1:26 - Possibly Outlaw Star
1:29 - Gundam Wing
1:31 - Definitely Dragon Ball Z: The World's Strongest
1:37 - Blue Submarine No. 6
1:51 - Animation is from The Big O. The voiceover is not. Google suggests it's from Gundam, but I can't pin it down. Possibly 08th MS Team.
The Toonami wiki page lists the shows used and the original air year.