Do you know of any well-known movies/shows/games that utilize After Effects?

The easiest examples I can think of are all from Andrew Kramer, as he has shared his work in the past.  He has worked with JJ Abrams on a number of TV and movie project, for example:

Star Trek: Into Darkness' title sequence was all done in After Effects, he made a video about it:

https://www.youtube.com/watch?v=AYzGhNkNBWs

He also made the title sequences for Fringe, Revolution(I thini it was called) and a THX promo loop - all in After Effects.

There's a whole slew of easily recognizable AE work. Pretty much every FUI (fake UIs on screens) in movies and TV shows is built on animated AE motion graphics and of course it's used regularly in similar capacity for creating animated maps and explainer graphics in documentaries. Recognizing other work would be difficult, though. You simply never know in which program VFX shots were processed, how much is genuine 3D work and so on unless it's explicitly stated by the artist and in making-ofs...

Mylenium

The animated phone numbers and web addresses on commercials like Luna and Feldco are quite obviously done in After Effects.