Overcast
When Marco Arment first released the Overcast podcast client, I bought it based on my experience with Marco's prior project, Instapaper. I like how Marco sweats the small stuff and I wanted to see what he'd do with a podcast client. However, I was not as immediately taken with Overcast as was most of the rest of the Internet. Also, at the time I was giving Apple's own Podcasts app a serious attempt. While the Podcasts app isn't going to knock your socks off, it does have Siri integration. I can be driving down the street and push the button for Siri and say, "Play Podcast Mac Power Users" and the app opens, and the correct podcast fires up. At the time I viewed that as the killer feature to let me listen to multiple podcasts while driving down the road. Also, Overcast didn't support the iPad or the Mac and I listen to podcasts on those devices as well.
After using the Podcast app for a month, I found that I'd only used the Siri integration a few times. Normally when I drive, I'm only good for listening to one podcast anyway. Also, in that interim period I discovered Overcast's ability to play podcasts on my Mac via the browser and the app also got iPad support.
All of this brought me back into Overcast and now I've been using a few months as my full time podcast player. I don't see myself leaving Overcast anytime soon. One of Overcast's banner features, Smart Speed, removes gaps and performs other tricks on an audio file so it plays faster without making the it sound too artificial or the hosts sound like they've been sucking helium. I'm finding myself using Smart Speed increasingly and now I'm not sure I'd want to do without it. Moreover, the user interface is just better than the other podcatchers I've used. The buttons are big enough to easily tap but not ugly or intrusive. I like the Orange color. The way it displays a live waveform is functional and kind of fun. In hindsight, most of the geeks figured it out before I did but I got there eventually and Overcast is now staying on my home screen.