Just to put in my two cents, but people will rate bootlegs as the 'best' for various reasons: sound quality, performance, setlists, etc. So, you will get different answers based on how you word your request.
As for Aarons list, he is spot on! Some of those shows are a little harder to find though.
Here's a list that I had put together a while back of popular (read: easy to find) bootlegs:
Another Time, Another Place March 6, 1981 Boston, MA excellent soundboard CDR (1)
Riverboat President Feb 11, 1982 & Dec 6, 1982 New Orleans, London very good/excellent audience CDR (1)
The Complete Boston '83 Tapes May 6, 1983 & Oct 14, 1980 Boston, MA and Holland excellent soundboard CDR (2)
Rattle and Hum Digitally Remastered Outtakes various various excellent professional recording CDR (2)
Rock's Hottest Ticket (Red Phantom) April 29, 1987 Chicago excellent audience CDR (2)
December XXVII Dec 27, 1989 Dublin, Ireland excellent soundboard CDR (2)
Dancing Zoo TV June 11, 1992 Stockholm excellent audience CDR (2)
The Real Thing June 15, 1992 Rotterdam good/very good soundboard CDR (2)
Zoo Europa August 28, 1993 Dublin excellent broadcast CDR (2)
Macarena Out of Control Sept 13, 1997 Barcelona excellent audience CDR (2)
Miss Sarajevo Sept 23, 1997 Sarajevo CDR (2)
Meximofo Dec 3, 1997 Mexico Excellent television broadcast CDR (2)
Viva Santiago Feb 11, 1998 Santiago, Chile good/very good broadcast CDR (2)
Blessed Are the Peacemakers March 29, 2001 Charlotte Audience recording by George W (very good) CDR (2)
I Remember You April 15, 2001 Portland Audience recording by GL (excellent) CDR (2)
The Last of the Rock Stars April 20, 2001 San Jose Audience recording by SG CDR (2)
The Cleveland Tea Party May 3, 2001 Cleveland ALD/audience recording (excellent) CDR (2)
That's Where I Lost You: New York June 17, 2001 New York Audience recording by SB (excellent) CDR (2)
Stronger Than Love & Pride July 18, 2001 Paris Audience recording by CV (very good/excellent) CDR (2)
(no title) July 21, 2001 Turin Audience recording by CV (very good/excelletn) CDR (2)
(no title) Oct 24, 2001 New York Audience recording by GW (very good/excellent) CDR (2)
When I Look at the World Nov 27, 2001 Kansas City Audience recording by AE (very good/excellent) CDR (2)