WMG / Planetarian

Planetarian is a prequel to Yokohama Kaidashi Kikou
Both take place After the End, both feature Ridiculously Human Robots (that are female, no less), the main characters of both series are leaning to cope with loneliness as they wait for their owners, and both main characters develop attachments for those few humans that stick around. Given the circumstances of either work, it should be virtually seamless to fit Planetarian into the same timeline as Yokohama Kaidashi Kikou depicting the final stages of the war that lead to humanity's downfall. The Planetarian robot would be an early Alpha-type of robot, maybe the same one buried under the grave Kokone ran into before she entered the library.

Planetarian also belongs to the same timeline as ARIA
If Yokohama Kaidashi Kikou is in the same timeline ARIA (like the YKK WMG page suggests) and if Planetarian also in the same timeline as Yokohama Kaidashi Kikou, than the rules of logic state that, therefore, Planetarian is in the same timeline as ARIA as well.

Planetarian is in the same universe as Wall E.
The Buy'N'Large Corporation was directly or indirectly responsible for the catalysts of the war. The war itself was the other reason as to the launching of the Axiom (though Shelby Forthright hid that reason from the unaware public because, you know, war. It'd crush their hopes.) and obviously, the wrecking of the Earth. However, BnL felt racist and decided to screw Japan (which was the only area plagued by the acid rain for some reason), thus why there are still some survivor remaining there. We can also assume that BnL helped in the development of Reverie and that at one point in his long life, WALL•E has taken her corpse into his stash of treasures.

Planetarian is in the same universe as Fallout 3
I'll let you draw your own conclusions on that one. Or, as someone from 4chan said upon encountering an abandoned planetarium in Fallout 3, "I was expecting Reverie, but all I got were super-mutants!"

Planetarian is in the same universe as Ever17
Specifically, it's the future that occurs after Takeshi's bad ending. The biological weapons that wiped out most of humanity were the result of Leiblich's perfection of Tief Blau. In fact, Leiblich's influence in most major governments was probably one of the major factors that caused humanity's self-destruction.

Planetarian takes place at the same time as Power Rangers RPM
Post-apocalyptic setting? Check. Killer bots that prowl every ruined city? Check. The endless rain? Venjix has the ability to bring down endless rain by messing with massive (country-wide) weather systems. And there's something in Reverie that prevents her from getting infected with the Venjix virus — that's for Doctor K to discover.

The Junker was Tomoya Okazaki in a previous life.
Not even gathering all light orbs could give him the strength for cancelling the apocalypse.

Planetarian is in the same universe as There Will Come Soft Rains.