I'd highly suggest the
Creatures Series. The games simulate a sort of Artificial Life, with the player breeding, observing, and interacting in a godlike fashion with a breed of critters called Norns, which share a world (or organic spaceship) with other creatures both friendly and hostile. The graphics can be a bit crude (more so in the older games) but the games are deep and complex, and though interaction with the world is encouraged, they definitely fit the bill for "Sit and Watch" games.
The series was designed half to be a sort of sandbox game, and half as an experiment in the complex modelling of genetics, biology, and ecology. You can teach them the basics of language (such that they can communicate with you and each other to the best of their ability), breed them for certain traits, or let them run amok on their world and watch them struggle, grow, breed, and die. It's really a gem of a game, and the simple premise belies something really complex and rewarding. It's got a level of complexity not unlike Dwarf Fortress, with the game modeling organs and biological systems, genetics, toxins and hormones, intelligence, learning, emotion, and more. It's definitely a unique title, and worth trying... especially since it's available for only $5.99 from GOG.com.
I love the art style of the first game... the world is stitched together from photographs and the occasional sprite, and feels kinda like an assemblage sculpture... which fits the setting, being that it's a ramshackle artificial ringworld created and then abandoned by a race of absent-minded scientists. The second is prettier, but rushed (apparently the Norn's brains are buggy unless patched; Norns can turn into vegetables due to an excess of reward chemicals rewarding them for their every action, preventing them from learning). The third is definitely the most polished, and though the world (an organic spaceship) is smaller and takes little time to fully explore, it makes up for it with a wealth of complex new gameplay, and far improved biological modelling.
Links:
A fairly decent Video Introduction to the series.Creatures 1 and 2, via GOG.comCreatures 3 with expansions, via GOG.com