My list is informed by the consideration of longevity and replayability, casualness, and challenge. These are all games that have stood the test of time and found a permanent home on my device and pose a significant challenge without requiring lengthy playing sessions.
This is an elegant and sophisticated Brough-like (i.e. a Roguelike by the incomparable Michael Brough). It incorporates several layers of strategy upon the original gameplay formula and is set within a beautiful system hacking themed environment. The game poses much difficulty and I have yet to complete it. I will probably be playing for many years to come.
Aptly described as the love child of Pacman and Rogue, this game features a charming pea-shooting Pixel. I do not know if the levels are actually randomized but it feels like I have never played the same map twice.
This is Taito's brilliant 21st century rendition of the classic Space Invaders and my favorite shooter. I recall playing a final Boss, but I don't know that I ever actually ran out of levels. The custom music generated levels also contribute to infinite replayability. I recommend trying a Canabalt-themed level.