The Global Imagery Browse Services (GIBS) is a great new API provided by the NASA to access its vast collection of Earth Observation products. For example the following URL allows you to download a jpeg picture of the Terra MODIS NDVI on 2018 Jan 01 over Africa:
By looping on the "TIME" parameter (in a bash script using wget) I could get all the available products from 2016-07-30 until yesterday, and make this animation (using ffmpeg).
— Simon Gascoin (@sgascoin) May 24, 2018
Each layer comes with a specific colormap that is consistent with the product. In addition you can download a stack of multiple layers with different opacities, for example you can overlay the MODIS "fire" layer on the "NDVI" layer.
It's convenient to use the worldview online data browser to get the right URL template. Just click on "Take a snapshot" and copy the URL. You can also download the images as Geotiff if you wish to combine them with other geospatial data.