For beginners (A1-B1 level), here are some websites, programs and books that I recommend you to start with.
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Free Online Programs & Videos
Deutsche Welle - Learn German (A1-B1)
This is a full course that helps you develop your vocabulary, learn some basic grammar rules and communicate in some everyday situations. You practice your listening, reading, writing and pronunciation skills.
German To Go (A1-B1)
It is run by a teacher named Juliane, she makes a lot of videos with English explanations and I like her style a lot. Very often, she explains things exactly the way I would. You can check the free lessons on her website. Otherwise she offers a very affordable package of video lessons that you can use for practice on your own and it takes you step by step through different topics from complete beginner to intermediate level.
Deutsch für dich (A1-B1)
The website of Goethe institute offers free of charge videos, interactive learning games, expert chat, forum and groups.
Harry - gefangen in der Zeit (A1-B1)
"Harry" is a bilingual, German course by Deutsche Welle, composed of 100 episodes. You'll find 400 interactive exercises online, a vocabulary trainer with more than 3,500 spoken words, as well as geographical information and ideas for lessons for all of the episodes.
Grammar course for Beginners (A1)
Tables, short explanations, examples and exercises help you with some of the basic grammar topics at the beginner level.
Grammar & Communication
Unsere Straße (A1-A2)
An interactive program by Goethe Institut that helps you listen and learn from everyday dialogues. As you move through the interactive street, you meet different people in their everyday routine and can "participate" in their dialogues, by continuing the dialogue and listening to them speaking.
Learn basic words with pictures
Pick a topic you want to learn, go over the picture and listen to the pronunciation. You can also quiz yourself to see if you remembered correctly all new words.
Hören & Sprechen (available for A1, A2, B1, B2)
Practice listening to slowly spoken dialogues and texts and answering or repeating the phrases. These books are avalable as print copy + CD or as a downloadbale PDF + MP3. Great for additional practice.
Books & Textbooks (to buy)
German Grammar Explained Easily (available in multiple languages)
This books explaines the German grammar in an easy way with practical examples. You can buy the book in German or in some of the other languages - currently available are English and Spanish.
An additional exercise e-book goes extra with the grammar book.