It's a somewhat awkwardly named museum, but Museo del Objeto del Objeto, has a charming, fascinating collection that tells the history of modern Mexico through both extraordinary and everyday objects it has made and used. Though it has a solid collection of objects, the museum features only temporary exhibits, all of which are geared to "promote the production of a culture of the unexpected and the uncommon."
Two hundred years and 100,000+ objects make for some neat exhibits, curated on topics as diverse as Mexican graphic design in the age of the Revolution and the highly-personalized toolboxes of shoeshine men.
The small Museo del Objeto del Objeto (Museum of the Object of the Object) is a Roma neighborhood gem. It strives to document the evolution of design and communication of the last 200 years through curious objects. You can find a Japanese beer ad from 1890, posters from rock concerts of the 1960s and many other insightful objects.