I no particular order. It fluctuates which is where based on whether a song from the soundtrack of one pops into my head or I start thinking about scenes and events from another.
Neon Genesis Evangelion: It's on a bunch of these lists for a good reason, and End of Eva is just...I didn't sleep a lot that night. Okay well I watched Barefoot Gen that day too but still. Honestly the series is so popular I can't say anything that hasn't been said.
Legend of the Galactic Heroes: The fact that it hasn't been listed in this thread is maddening. It's long, sure, but when it comes to exploring political themes through a two sided conflict that puts good amount of focus on all sides through compelling characters, and doing so well at it, I mean, it's not 'The Wire of anime' but...actually it is and you should go watch both.
Madoka Magica: I watched this in one day and my mind was on it for the rest of the evening while at work, and some time after. Episode 10 in particular is just perfect.
Kaiji: While slow paced, it excels in using that to its advantage, mounting tension splendidly, especially season 1. It tops out the likes of Liar Game and Death Note for me easily as far as mind games and battles of wits. E-Card in particular stood out, but the rest of Season 1, the second season, and the still ongoing manga, even the authors other works like Akagi and Zero are also excellent.
Chihayafuru: When the opening alone gets you hyped for the episode and the ending theme brings a groan as you realize you have to wait for the next episode (especially season 2 where it was a week away), well, that doesn't happen that often for me. It's not as dark or serious as the above, but it's well executed with likable characters, so I found it highly engaging.
Honorable mentions: Ping Pong the Animation (the animation might be a bit off putting, but I found it engaging and the character arcs were well done), Aria the Origination (even the 'worst' episodes were at least a 9/10. I disliked the occasional change from the manga, but it's still wonderful)
