Here are some personal recommendations from Thomas and me: Danish items which will help to improve both your language skills and knowledge of Danish culture (Check back for updates)
Books

This book is aimed at total beginners. It will take you through all the essentials to an intermediate level of Danish with help of fun stories, interesting dialogues, sound files, and a variety of tasks. Head over to the store to check it out.
I personally have this book in both Danish and Spanish, and although I don´t use it as much as I could, it is very useful and a perfect size to carry around in your pocket or bag.

This is a textbook which I recommend for intermediate to advanced learners who really want to improve their academic Danish. Topics in the book include: economy, environment, media, language, and more.
Buy it at Saxo.dk

Books by Jakob Martin Strid. Some are rhyming books, some comics, mostly aimed at kids, but I really think you can appreciate these at any age. They are interesting, the illustrations are amazing. I think you should check them out. Here is a link to his website.
Mustafas Kiosk is one Strid's best rhyming books. It's full of interesting word and rhymes to inspire your Danish. This is actually a link to an audio version of the book, and it's worth every cent.
I haven´t read this book, but my wife has told me how great it is, so if you´re looking to get into the Danish hygge, check this one out!
More text books
Videre mod dansk (upper beginners)
Pæredansk (Intermediate learners)
TV and Movies
Mofibo recommendations
Vikingevenner series (low intermediate)
Træts hemmelige liv (Advanced)
Dyrenes hemmelige liv (Advanced)
Harry Potter (På dansk) (Intermediate)
Sapiens (Advanced)
Nordisk mytologi (Intermediate)
Vigingernes helte (upper-intermediate)
Aktivt kreativ
Hvor taler du flot dansk
Den iranske gartner
Forbrydelsen
The killing is one of the first series to break out of Denmark. Super popular in the UK, it´s a long and dark drama which keeps you guessing: three series, each with one case which becomes solved in the final episode. Amazing.
Dicte
Dicte is a personal favorite of mine. It´s not as dark and broody as The Killing, but still has the cool, dark edge you'd expect in a Danish crime series. Grab it here on Amazon or check it out via the TV2 play app if you are living in Denmark.
Klovn
On a lighter note, here we have the Klovn series. The first few are without English subs (last time I checked)-more reason to learn Danish, but it is a must see if you want to laugh and get inside the Danish humor. Every Dane is familar with this if they like it or not. New season expected in 2018.
Blinkende Lygter
Next up, we have a classic: "Blinkende Lygter" or Flickering Lights: a crazy funny movie starring some of Denmark´s heavy weight actors. One of my favorites. Some gangsters steal cash from their boss, find a cabin in the woods, which they decide they like and want to turn into a restaurant. Climactic ending!
Mænd og høns
Stay away from this one if you have a weak stomach. Give it a spin if you have an interest in all things totally weird. Freaky in a way you won´t be able to look away.
Jagten
This is also not one for the sensitive, but it´s well made - another movie with Mads Mikkelsen, who we all know is one the best (probably). He is a falsly accused teacher who eventually finds out the truth. Great movie.
If you're not so into the 70's, here is a moderne take on Olsenbanden in the form of animation. I think this movie is great.
Terkel i knibe
Another animated series, this is just the best. Full of cultural references (see Jul på Vesterbro), great music, great animiation and interesting characters. I recommend researching Anders Matthesen, if you don't know him. He is a personal inspiration for me.
Netflix recommendations
More Danish movies
Here´s a playlist of some of our favorite animated movies and series on YouTube
Rita
The Rain
Alle for én
Klassefesten
Ronan Barbaren
Broen
Copenhagen
Der kommer en dag
En kongelig affære
Player
Pusher
Adams æbler
Efter bryluppet
Flammen og citronen
Dreng
Elsker dig for evigt
Blå mænd
Camping
Brødre
Direktøren for det hele
Vikaren
Sorte kugler
Den eneste en
Sover Dolly på ryggen?
Superclásico
En chance til
Sommeren ´92
Klovn forever
Rita
If you´re looking for something more modern and accesible, get binging on Netflix with Rita. This has been the hottest series of the past few years and has it all: Drama, comedy, culture, you name it.
Arvingerne
Another great Danish drama based around a family who after losing their mother must pick up the pieces and cooperate. The family home, originally intended to be equally divided between three, is instead left to a fourth child. I would translate the title as "The Heirs" as at arve is to inherit.
Olsenbanden
Didn't see any of the Olsen stuff yet? you're in for a treat. The classics are from the 70's, full of cultural references and fun plots. One of my faves, the gang go to Jutland to find hidden treasures in a German bunker.
Sover Dolly på ryggen?
Fun romantic comedy- Danish style. A woman gives birth to a baby with help of a sperm insemination, gets curious about who the father is, and sets out to find him. Plus Nikolaj is a legend!
Other Nordic series
Trapped
Fortitude
Dem som dræber
Hjerteløs
Riget
YouTube Channels
Apps
Great app for beginners and advanced learners. This has a huge vocabulary range and a number og games/methods to help you remember some of the most important Danish words.

DR Nyheder (DR News) is for you if you like current events: follow stories in and out of Denmark and recieve notifications so you never miss a thing- and of course great practice for your Danish.

Best app for Danish reading. Here you´ll find a huge range of books at all levels and genres both as text and audio books.
I've been though a huge list of translation apps for Danish language and this has been by far the most accurate. So long as you speak clearly, 8 out of 10 times this app will get it right. Great for prounuciation practice and translations.

Blockbuster is still going strong in Denmark. You can rent, buy and stream all the big movies with Danish subs and catch a load of nordic releases inside the app.

Viaplay is a great app for movies and series. Here you will get both Danish and English/American stuff, all with Danish subtitles. Well worth the subscription.

One of my favorite apps for Danish tv and movies. 99 kr. per month gives you full access to 10 live channels plus on demand series, movies, sport, and more.

The DR tv app is totally free, no subscription needed and you get to see a wide range of Danish tv, series, news reports, and more. Must have app!

Højtlæseren is a audio book app for kids. Although there isn't a huge range available right now, the books that are there are interesting, well read and great for beginner and intemediate learners.
FB Groups
Online sites
Videre mod dansk lydfiler (Further towards Danish sound files)
På vej til dansk lydfiler (On the road to Danish sound files)
My good friend, Birgit Månestråle, offers a number of great services for Danish learners including walk-and-talks and email lessons. Birgit is also educated in psychotherapy and can offer you both objective and practical advice, whatever the subject.
For more information, visit: www.learndanishwithease.dk or www.birgitmaanestraale.dk/en
Music
Here's a nice Danish playlist we've put together on YouTube featuring some of our favorite artists. Save and check back for regular updates and new additions.