0:00 - 0:28 - The Big O.

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. No idea if the explosion is also taken from there.

1:10 - Gundam Wing

1:14 - Probably the original Batman animated series.

1:16 - Dragon Ball Z, probably the film The World's Strongest

1:26 - ???

1:29 - Gundam Wing

1:31 - Definitely Dragon Ball Z: The World's Strongest

1:37 - I believe this is Blue Submarine No. 6.

1:51 - Animation is from The Big O. The voiceover is not, and I don't know where it would be from.

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.