I cannot possibly pick just one favorite TV character, so I'll have to give a list, starting with, to my adult fangirl embarrassment, Mr. Spock. After him are...
Dr. Quincy from Quincy
Susan Ivanova from Babylon 5
Elam Garek and Kai Opaka from Deep Space Nine
Dr. Sam Beckett and Adm. Al Calavicci from Quantum Leap
The entire cast of Bones, including Zack
Aaron Hotchner from Criminal Minds
Nurse Carol Hathaway from ER
Col. Samantha Carter from Stargate SG-1
Caleigh DuQuesne from CSI: Miami
Rick Castle from Castle
The entire cast of Firefly--though I'm not all that fond of Simon.