From there I like Coffee Break German because it has a language expert and a native speaker discussing German words and grammar in a classroom/conversational setting. Again, this one is narrated in English but they're talking about the German language.
DaZPod is also great for short little clips, completely in German. Once you're ready for the full-on German stuff, Langsam Gesprochene Nachrichten has a new podcast every day where they read world news, slowly and clearly articulated, completely in German.
Of course most of these come with transcripts you can read along with to improve your German reading comprehension as well.
-edit: check out DW.com and look for their German courses... they have a ton of podcasts for all levels, and they're really good.
If you don't mind listening to a really weird drama about a hotel porter who's having some kind of psychotic episode. I'm not knocking it, but it's bloody strange.
The presenter speaks slowly (as the name suggests) and clearly, and there are over 100 episodes on a variety of topics, so there's probably something to suit your interests and level.
Deutsche Welle also have podcasts and videos at various levels and you can download a slowly-read news broadcast ("Langsam gesprochene Nachrichten") every day: http://www.dw.com/en/learn-german/s-2469
Or for a normal speed news broadcast for native speakers, you can subscribe to ZDF's "Tagesschau" or "Tagesthemen" podcast, or watch a video of "news in 100 seconds": https://www.tagesschau.de
I'm also interested to hear more recommendations!
NOS Radio 1 also has a daily podcast 'De Dag' (https://www.nporadio1.nl/homepage/8030-podcast-dedag-quote).
These are not really for beginners though.
Another general news site is http://www.nu.nl. Lots of short news articles, often from press bureaux. Easy to dip into for a few minutes.
When I started learning Dutch, I initially found it very hard to relate the sounds vs written words. My approach for listening comprehension was find a short news story with accompanying written text, and simply listen to it over and over again, alternating with the text and without, gradually getting used to the sound and flow of the language. My approach for speaking was careful repetition of sentences from language courses.
Good luck!
Year #1 - Self-study with books/audio courses. Got me up to reading simple newspaper articles, struggling with TV news.
Year #2 - Started with a week-long residential Dutch course. It felt like I didn't learn much new grammar or vocab, but suddenly I was thinking in Dutch, no longer mentally translating. Very expensive but definitely worth it. - Then my company (management consultants) decided I was ready to work full time in Dutch with Dutch clients. The first month was very tiring: I felt 20% IQ points dumber, and could either listen or speak in meetings, not fast enough to do both at once :)
Year 3 - After that, I was ok working in Dutch and speaking it socially.
Year 4 - By the time I left the Netherlands, I was managing a team of 25 Dutch people, doing meetings, performance reviews in Dutch.
I subsequently ended up marrying a Dutch guy. While we left the Netherlands 7 years ago and now live in London, at home we speak probably 30% Dutch/70% English.
Dutch was never a language I expected to learn. But I am very glad I did. The sounds of the language still make me smile :)