As their name suggests, forever (or evergreen) games are games that don’t have a finale or culmination, as in “The End”. These games have a very high replayability factor (meaning we enjoy playing them over and over again).
Forever games are also timeless. We can pick up these games anytime , be it the day they were released, or a few years later, and play them for months or years. We can even stop playing for a while, pick them up again years later, and they’d still be fun and relevant.
I suppose Dwarf Fortress would qualify, but I tend to get tired of everything sooner or later.
Minesweeper and circloO was good to play on my phone for a few weeks when away from my PC.
Oh and almost forgot about Caves (the traditional rogue-like on Android). I occasionally come back to that one, but get frustrated pretty quick now.