Being a native of Kansas City, I'm very biased when it comes to BBQ. I truly believe we have the best in the USA.

Here are my picks:
Kansas City Area
#1-Arthur Bryant's (Yes, the do have one located in Terminal A at MCI, however, it's NOT the same experience and food quality as what you'll get at the downtown location).

#2-Smokehouse BBQ
#3-Gates BBQ
#4-Jack Stack
#5-Wabash BBQ (Excelsior Springs, MO)
#6-Winslow's City Market BBQ
#7-Oklahoma Joe's BBQ

#8-Wyandot BBQ

Elsewhere in Missouri
#1-Three Pigs BBQ (Lake of the Ozarks/Gravois Mills, MO)
#2-B&P BBQ Pit (Lake of the Ozarks/Sunrise Beach, MO)
#3-Brown's BBQ (Clinton, MO)
#4-Rib Shack BBQ (Springfield, MO)

Oklahoma City Area
#1-Dale's BBQ (Moore, OK)
#2-Oklahoma Station BBQ
#3-Larry's Rib Pit
#4-Crockett's Smokehouse (Midwest City, OK)