I have three CDs of Hume's music, all of which are pretty good:
is all solo viol music played by Jordi Savall, including the jauntily titled "My Death", which appears to quote from "As Time Goes By". It's a rerecording of the same repertoire as the solo disc mentioned in Ron's link.
I also have the other two: Savall's ensemble Hespèrion XX recorded a disc of vocal and chamber music, of which the highlight for me (if that's the word) is the lugubrious "Alas poore men" for baritone and bass viol (it also contains "Tobacco", Hume's song of praise to the weed, but perhaps I shouldn't mention that). And the third is by Emma Kirkby and the ensemble Labyrinto, which overlaps somewhat with both of the others. There are some newer recordings on Naxos which I haven't heard.