Ani-Monday, on Sci-Fi Channel / Syfy
This is certainly not the first time Sci-Fi Channel ever aired anime, and probably not the first time I ever saw anime on that network, but it's the first time I specifically remember doing so. The late night block began in June 2007, and in February 2008, Sci-Fi began also airing anime on Tuesday nights. In July 2009, a block also called "Ani-Monday" began airing on the Chiller network, which I didn't get, so I couldn't watch any of that. (This was the same month that Sci-Fi Channel changed its name to Syfy.) In March 2011, "Ani-Monday" was moved to Thursday nights. (I'm thinking the Tuesday and Thursday slots weren't called "Ani-Monday"; one would guess "Ani-Tuesday" and "Ani-Thursday," but I really don't remember.) Whatever the blocks were called, they ended in June of 2011. (It was about that time that I lost access to Syfy, anyway.)
There were lots of things aired on Ani-Monday (or Ani-whatever-day-of-the-week) that I never watched, but I did see several things there. They included Dead Leaves (OVA), Gundam 00, Gurren Lagann, Kai Doh Maru (OVA), Monster (though I didn't get to see the whole series), Noein, Now and Then, Here and There, Rave Master (which had previously aired on Toonami), and Tactics. I started watching Chrono Crusade, but I think my DVR messed up the recording after the first couple of episodes, so I quit (and later watched the series on DVD). And I think that's probably everything I watched on Ani-Monday (or Ani-whatever-day).