This 2007 No.1 compilation released at the time of the 30th anniversary of his death captures 52 great Elvis tracks with a good representation of material from all stages of Elvis's career.
One thing slightly different about this compilation is that the hits are not arranged in chronological order. All the standards you might expect are included, but in addition there are there are a few minor hits (if there is such a adjective) that normally don't make a greatest hits compilation and the odd album only track. So for example, "Fever" from the "Elvis is Back" album of 1960, "Green, Green Grass Of Home", a top 30 single from 1975.
If you are looking for an Elvis greatest hits compilation Elvis 75 from 2010 is the most comprehensive. A top 10 release that coincided with what would have been Elvis's 75th birthday.