The types of imagery you've listed are from a number of different sources, and it might be difficult to find all of them from one place or for free (but there might be a repository that makes this easier for you. I know of a few for imagery of the polar regions - Polar Geospatial Center and Alaska Satellite Facility).
As @jpmaniac87 said, USGS will provide pretty easy access to the Landsat suite of sensors as well as MODIS, which should have a [coarse resolution] DEM for free. Imagery from other US owned satellites should also be freely available, but repositories vary. I can't provide any input on PalSAR, and I personally have had issues getting imagery from SPOT (I believe imagery five years and older should be free to the international community). The European Space Agency (ESA) also has some freely available imagery, which I believe includes radar datasets. There are many other observational satellite datasets out there, but these are just some of the ones I know best.
Your question is challenging to answer specifically without additional defining characteristics besides "for free". What type of imagery are you looking for (radar?, optical?, one of each? images from the four specific sources you mention?) and what type of spatial resolution do you need? Also, does it matter when the scene is from?