A list of resources for learning Chinese with updates based on previous comments. Open source software is listed in bold
Learning Apps
HelloChinese - similar to Duolingo, has adapted reading and flashcards, only HSK 1 level content is free
Duolingo - does not need introduction
Du Chinese - adapted reading, few lessons are free
Flashcard Apps
Anki has mobile, desktop and web versions
TOFU Learn - mobile app that supports writing Chinese with touchscreen
Wuxia Learn is WIP, some people may find it useful
Dictionaries
Pleco has a great mobile version
MDBG has a decent web version
Dong Chinese Wiki has character etymologies making learning characters easier
Hanbook calls itself a dictionary with smart learning
Language Exchange
Youtube
ShuoShuoChinese兑兑中文 has lessons for levels up to HSK4, interviews in Chinese, entertaining content
Grace Mandarin Chinese has amazing unstructured lessons with both traditional and simplified characters, slightly focused on Taiwan, China
Everyday Chinese has a lot of "Real Chinese Conversations" for beginner language immersion
Mandarin Corner has street interviews with subtitles (pinyin & translation included), perfect for HSK 3 immersion, speakers can have provincial accents
Chinese Zero-to-Hero has high quality Chinese grammar lessons for all levels HSK 1-9
Movies, series & cartoons
领风者 / The Leader on Youtube is an anime series about Karl Marx, requires good Chinese
Born To Love You (2013) on YT is a romantic movie
Peppa Pig available on Youtube but no subtitles, all inclusive for family, HSK 2-3 language
iPartment available on Youtube. Review from another Lemmygradian: "It's a sitcom based in Shanghai and is pretty Western, so you can understand what's going on even if you don't speak any Chinese. Read the synopsis on Wikipedia if you're in this boat. I watched it before I passed HSK 1 and picked up a few things, but there's certainly value to just listening and getting used to how spoken Mandarin sounds. I went back once I passed HSK 4 and started watching it again and was able to understand a lot more of the "Why" things were happening"
I also highly recommend the channel Lazy Chinese - Comprehensible input . The beginner series are excellent.