There are...so many out there. I've listened to a number of them myself, and enjoyed some more than others. I thought I'd mention a few and my thoughts - pipe in with ones you've listened to, both good and bad!
Adventure Zone - Balance Arc
It wouldn't be a D&D podcast list without mentioning the pod that got a bunch of people I know interested in running a game. While the McElroy's recent attempts at RP arcs with this pod have been lackluster at best, this first arc was really a treat. Griffin (the DM) composed his own music for the various settings, the arc had well framed chapters where the characters found themselves in entirely different landscapes. Always willing to bend the rules for some interesting content, the finale ends up much less as a D&D session and more as a fantasy book playing out before you. There are some tear-jerking moments towards the end; the McElroy family does an excellent job of cultivating characters you can't help but root for. As mentioned earlier their more recent attempts found me wanting and I realized my podcast queue had higher priority items I'd rather stock it with.
Crit Juice
I believe this one was a recommendation from @MisterPookie at one point, but I gave the 5E arc a listen. They had a large cast and I was pleased with the diversity and creativity that each of the characters had in the first few episodes. Unfortunately their 5E arc is only 5 episodes and the last one came out in 2017, so no new content there. But some lovely drunk D&D moments are immortalized in this pod.
Godsfall
You know it's going to be a high production value D&D pod when the first two episodes are the DM explaining the lineage and history of the gods within his world. This podcast is the work of a DM who has been at it for years who isn't afraid of spending several hours re-listening and re-editing an episode to make it perfect. It's filled with sound clips which help make the story come alive. While it has its funny moments and the lore runs extremely deep, I ultimately dropped this pod from my list because it was quite serious and I felt I couldn't stop paying attention for even a second lest I miss some crucial minor detail. If you want to be immersed in a rich and enthralling world, this is the pod for you.
Day Players
@milkmonger has a podcast!! And it's good as hell go listen to it!!! Their schtick is that they sit down for a session, make (mostly) random characters, and the DM improvises the entire session for the players. I love listening to this pod because 1) my dumb girl brain doesn't have to remember as many details because the sessions split into about 4-6 episodes each arc and 2) it allows for the team to do try some really creative tactics out that wouldn't otherwise be viable in a longer running campaign. Case in point - their "Smite Club" arc, where all PCs play paladins on a quest to rid evil out from a town. I also love hearing my friends be funny on a pod. Give this one a listen! Although I'd suggest starting anywhere but the first arc, it's a little rough. They get their groove shortly after that and the rest are just a blast.
Not Another D&D Podcast - Trinyvale Arc
Another recommendation from @MisterPookie, although I'm only a few episodes in. This one is just fun fun fun. It's lighthearted, it doesn't take itself too seriously, and it's a D&D breath of fresh air. Probably the antithesis to Godsfall IMO. It's got a few of the old CollegeHumor gang on its cast. Trinyvale is a strange half-fantasy half-steampunk world filled with adventure, drinking, and butt jokes. If you're not looking for something too engrossing but still hilarious, this is the one for you.
I think that's all I can recall for now...there's more out there though, since everyone has their own D&D pod. Add the ones you've heard below!