Those singers you enjoy,....that don't really have a great voice?

Glenn Gould...he hums along with his piano but I still like him.

Billy Gibbons has a great voice by the way, as does Elvis Costello and many others listed here. What's the standard? Opera? A great voice is one that gets the point across mostly in tune...serves the song as it were. Lots of so-called  "great" singers don't get that done, so I'll take Johnny Cash all day...an actual GREAT singer.

Keith Jarrett hums too, and like him also.

I agree for many of the above mentioned but i would add Jim Kerr who just makes meaninless words from vowels just to fit in the pattern.

Ozzy does not have a great voice but is mostly enjoyable (Sabbath period), as is Iggy Pop, Neil Young, Brian Johnson, Joey Ramone, Anthony Keidis, ...

Of course i am not enjoying Yoko.

By my ridiculously unscientific calculations, it can be stated that approximately 80% of all singers can be put in this category.

Randy Newman

Randy Newman.  But his lyrics compensate for his voice,