Note for German-speakers:
One quick note before I start presenting the links: many people are inspired to learn Dutch because they already know German. Although knowing German gives you a nice head start, it doesn't mean that Dutch and German are the same language or that you will be able to learn Dutch without really trying. There are significant differences, especially when it comes to speaking and pronunciation.

If you speak German, I particularly recommend that you try to find native Dutch speakers, or at least people who do not speak German, to practice with. It is all too easy to start inventing Dutch words based on your German vocabulary, and if your interlocutor also speaks German, they are likely to "understand" your made-up words and not call you on it. Before long, you'll both be speaking some bizarre German-Dutch hybrid. See this site for German-Dutch "valse vrienden."

Sites to start with

  • Free wikibook introduction to Dutch
  • The Integral Dutch Course has, in various forms, been floating around the internet for many years. While I don't think it would be very useful for learning to speak Dutch, it might be a good way to get a feel for the grammar, especially if you're comparing it to German.
  • The Taalthuis site offers beginner and intermediate courses that, while brief, could be a good starting point.
  • This site apparently offers online Dutch language classes. However, I've never taken any and can't vouch for the site.

Drills and quizzes

References

Where to meet and work with other people learning Dutch