Here is a quick list of the podcasts I quite enjoy listening to apart from the Bombcast. 
  

1.  Idle Thumbs 

Idle Thumbs consists of vaguely videogame related discussion by thes fools: 
 
Chris Remo, of Gamasutra 
Nick Breckon, of Shacknews 
Jake Rodkin, of Telltale. 
 
It's one of the silliest podcasts about videogames that I've heard.  They often have comedy music thrown in there too. 
 
 

2.  The Rock, Paper, Shotgun Electronic Wireless Show 

Rock, Paper, Shotgun is an interesting little website focused on PC games.  Their podcast has this weird leapfrog way of going about. 
 
One week would have the Bath-based John Walker and Jim Rossignol. 
The next week would have London-based Kieron Gillen and Alec Meer. 
 
Kieron and Alec have seemingly missed their turn for the last few weeks, but the John and Jim's intelligent fortnightly babble makes up for it. 
 
 

3.  Rum Doings

Rum Doings is a new podcast also with John Walker, this time joined by his friend Nick Malier and NOT ABOUT VIDEOGAMES.  Their idea for this was to have a podcast that was entirely off-topic.  They choose a topic and then try their best to avoid it.  It's quite funny if a bit mad.
 
Episode One here. 
Episode Two here. 
 
And that's that, 
SlowHands.