Favorite and come back when you need a new show

Let's start with the current big boy in audio theater.

One of the top rated podcasts on iTunes.
Listen to the community radio updates from a town where everything is normal... if you consider normal to be angels that live with the local spinster, a dog park you're not allowed to think about, a five headed dragon running for mayor and weirder stuff than that. All of which the town's folk seem to accept like business as usual. Most people that listen to podcasts have at least heard of this show but it has to be on this list. If you haven't given it a try you really should.
http://www.welcometonightvale.com/

The first block buster hit of podcast audio drama.

A year before The Walking Dead appeared on television this award winning show was blowing up the podcast charts. While the monsters aren't really zombies the story follows the modern zombie story format. This is a tale about a group of people trying to survive in a world that's actively trying to kill them. The acting and audio effects are done very well.
Clocking in at about 200 hrs the story has been completed, reaching it's originally planned conclusion. No worries here about getting into a podcast and having it end abruptly for a lack of funds. My only complaint is the "Stephen King" style ending that seems to happen too quickly and not completely satisfyingly. Though, like a S. King book, the end doesn't stop me some recommending it.
If you're thinking that you don't like horror stories, that's not what this is. It's a drama. Give it a try.
Bonus for the fans; A spin off "Lock Down" is already in the works and principle recording is done.
http://www.werealive.com/

Time for something a bit more fun.

Our podcaster has fallen through a dimensional portal behind the Burger King and still has a slight wi-fi signal so he's doing a podcast from a tavern in the magical land of Foon. Listen every week as Arnie and his friends (a magician and a shapeshifter with a thing for badgers) interview the locals. Order a spicy potato or ale and meet amorous goblins, imps that poop coins, a flower with a really bad attitude and other citizens of the land.
If you like fantasy and comedy give this one a try. Much of the dialog is improvised but it never fails to amuse. The show is done in a talk show format so it's light on the audio effects but you won't really miss them.
http://hellofromthemagictavern.com/

Get your spooky on.

A journalist starts to cover a seemingly innocent story and quickly finds herself involved in a series of supernatural occurrences and mysteries. The show has an "X-Files" like vibe with new mysteries every episode, that may all have a common thread, being investigated by a believer and a skeptic. The use of a format similar to NPR shows like "Serial" works to great effect.
Normally I'm not a fan of suspense tales, it's very rare for me to find one that actually spooks me. This one has made the hair on the back of my neck stand up, a few times. Only twelve episode into the series and I'm already hooked.
http://theblacktapespodcast.com/

Above and beyond the usual fan productions.

Parsec Award winner and running regularly since 2009 the monthly episodes are all around quality. Acting, story, incidental music and effects are all top of the line. You don't have to be a Trekkie to enjoy this show.
"In the darkest reaches of the United Federation of Planets, an isolated station stands sentinel over a neglected frontier. Commissioned long ago with high hopes, its promise is now all but forgotten. A lonely outpost serving as a gateway to the vast expanse beyond... where discovery... and adventure... await." The opening lines of each episode is a pretty good description. Stories are based around the crews of outpost Deep Space 3 and the USS Chimera.
This is the first time since ST the Next Generation that I've looked forward to new episodes of a Star Trek show. My personal favorite is the shakespearean comic relief of two ferengi brothers but there's plenty of action and drama. If you didn't know this was a fan production you'd assume Paramount studios got into the podcast market.
http://giantgnome.com/our-shows/audio-drama/star-trek-outpost/

Closest to a book with actors and effects.

Starting in modern day New York and progressing to an ancient city deep in the ocean, the protagonist discovers that immortals are real and she quickly gets entangled in their civil war. Based on a book with a strong fan base the story leans heavily on exposition. It has the feeling of an old-time radio detective story. This is the one on my list that people tend to either love or hate.
It made my list because it has a pretty large fan base so I want to point it out for the people that will give it a try and love it. So far there are over 40 episodes with more in production so it seems safe to assume it will reach it's planned conclusion.
http://www.leviathanchronicles.com/

The sci-fi parody you always wanted.

A comedy based around two mal-adjusted doctors and the odd-ball crew of a space station. The actors are doing a great job while the characters are interesting and well written. I found myself sucked into this story pretty quickly.
If Leviathan is the starter of internet fights, EOS 10 is the love fest on the review sites. It's quickly earned a loyal fan base. The show has completed two seasons (twenty episodes) and looks to be on track to raise the money for the next season.
http://www.eos10.com/

A relatively short drama.

In 2004 over 300 people at the Limetown research facility seemingly disappeared over night. Now an investigative journalist is assigned to do a "look back" story that leads to shocking new evidence. Follow the story as a long standing cover up starts to unravel.
A neat thing about the resurgence of theater of the mind is that people are still playing with the form and experimenting. This one is sort of the mini-series of the group, comprised of only seven episodes. Only three have been released as of now but the show has already gotten ratings that would have been unheard of a few years ago. It's very heavy on acting ability with some very good performances.
http://www.limetownstories.com/

The current Parsec Award winner, dark humor done right.

After a mishap with his "ultimate" weapon rips the fabric of the universe a scientist tries to repair the damage, along with an IT guy that he kidnaps from a doomed dimension. With the help of an AI laboratory, a sentient Higgs-Boson particle and others they visit alternate timelines and other dimensions. Of course the doctor thinks it's very important that they report their progress in podcast form, for reasons that don't really need to make sense.
This one reminds me of the fun old-time radio theater that I listened to on cassette with my grandfather, but with a completely modern sensibility. The story has some really dark elements but manages to be silly and funny.
http://www.hadrongospelhour.com/

Wrapping up with a podcast by a fellow imgurian.

You may have seen the post by @CarelessGamer here http://imgur.com/gallery/pzrNW.
"Liberty: Critical Research is set within the universe of the upcoming sci-fi comic book series, Liberty!" I'm actually glad I've heard this before being introduced to the story elsewhere. "Embark on a dangerous expedition into the unknown... Follow Dr. Kovski’s [paramilitary] team into the Fringe, the lawless sector of a war-torn space colony."
The episodes are short but they are well structured to keep you wanting to know more. Production quality is good. I'm looking forward to more.
https://nerdyshow.com/liberty/