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.
Tip: 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.