I'm trying to find this anime's name in this video at the 9:25 mark, anyone have any idea?
Gallifreyan is almost correct. It's from Ghost in the Shell 2: Innocence.
The modelling of Batou shown in the clip is older and has a gaunter face than the Batou of Stand Alone Complex. Moreover, Togusa (the guy on the right) has darker hair and less rounded eyes than his SAC counterpart. This is the drawing style of the movie Ghost In the Shell 2: Innocence.
It's a sequel to the original Ghost in the Shell movie, which was widely acclaimed for being a game changer in anime.
That said, I highly recommend watching GITS:SAC if you want a longer experience than the movie medium can provide. It's a great show, and both the show and the movies deal with great topics.
The guy with the glasses on the left is called Batou, and is instantly recognisable.
Sadly, I don't know which season or episode this is. If you're willing to get into the GitS universe, you may find this Q&A on Anime & Manga or Suggested starting place for Ghost in the Shell on this site helpful.