Geppy X
It's a 2d shooter with mechas but structured as a tv show. Each stage is like a tv episode, with Op, ED and even fictional commercials half-way through created expressively for this game.
Top notch voice work, great animations and plenty of 2d gorgeousness.
These are the op and ed
http://www.youtube.com/watch?v=U8_IPJ60B3Y
this is actual gameplay from the first chapter
http://www.youtube.com/watch?v=jU0U33Pe0Pg
(the commercial is 4:19)
Ace Combat 3 as other people already mentioned was one of my favourite games of all time.
Animation and screenplay were made by Production I.G and the entire plot was about political intrigue and artificial intelligence imitating life. Some topics were very close to Ghost in the shell in terms of content, but gladly they were all developed in a different direction.