The first analogy that comes to mind is probably between a building’s structure and an organism’s skeleton! While a building’s structure serves the same role as a skeleton in that it holds it up, some buildings have especially skeletal designs. For example, many have remarked before that the complex, interwoven trusses of structures like the Eiffel Tower is reminiscent of the spongey, porous network that makes up the interior of bones, especially like those of birds.
Another easy analogy is between solar panels, an increasingly common sight on new constructions, and leaves! I’d say this includes both photovoltaic panels and solar water heaters.
I would also draw an analogy between electrical utilities and the nervous system (since both run on electricity and allow a building to be controlled), plumbing and the circulatory system, and HVAC and the respiratory system.