A good host. See: Ben Hanson from GameInformer
I also really like podcasts that respond to listener email/tweets, have dedicated segments but aren't too strict about sticking to a certain agenda, and have co-hosts that know their shit. For example, the difference in knowledge between NVC host Jose Otero and his successor Filip Miucin was night and day.
Also, obvious passion for gaming, lack of fanboy-ism, a variety of different viewpoints among cohosts, and a fun game at the end that listeners can play along with like 20 Questions on GameScoop!
Besides the ones I mentioned, my current favorites are:
8-4 Play
Player One Podcast
Podcast Beyond!
Retronauts
Power Pros
GameXplain podcast
Kinda Funny Gamescast