Currently this year, these are the teams still alive to match the record

LA Clippers - 24-6 (Winners of 16 straight)
Oklahoma City - 22-6
San Antonio - 23-8
Miami - 20-7
New York - 21-9
Memphis - 18-8
Atlanta - 19-9
Golden State - 20-10

Also, for the worst record ever for a FULL NBA season, which is 9-73 by the 76ers.
Washington Wizards - 4-24
Cleveland - 7-25
New Orleans - 7-23
Charlotte - 7-23 (Losers of 17 straight)