At the moment, the best course for absolute beginners is probably "Ana Pana" at Lernu, an 8-lesson course with sounds, interactive exercises, etc. Teaches somewhat few words per lesson, but you can go through the lessons very quickly and pick up more words from original material or from the continuation course "Ana Renkontas" afterwards. Tutors are available for free.

If you know German, the KEK course (Kostenloser Esperanto Kurs) can really be recommended. It can be found here. It has 10 lessons, which are quite extensive. A free tutoring service is also included. After completing this course, you should have a very good level of Esperanto, since it teaches not just all grammar but also a lot of vocabulary and each lesson has two lesson texts. On the down side, there is rather much grammar taught very quickly: the first lesson presents almost all basic grammar for passive knowledge already, later lessons elaborate and actually teach it and past lesson 5 the grammar sections are mostly just revision. Another down side is that this course was developed for teaching through mail or e-mail, so there's no multimedia.

If you like Assimil-style sentences with translations and few explanations, Lernu's "Vojaĝu kun Zam" is for you.

If you are a fan of the "direct method", which says that you shouldn't use your native language at all, use the "Bildoj kaj demandoj" course at Lernu.

If you aren't fluent in any language besides English yet, or if you don't know grammar terms well, you might like the online textbook "Esperanto for non-grammarians". It teaches grammar really slowly and explains it well for people who never heard of terms like "noun" and "adjective". It also teaches a good amount of vocabulary. Unfortunately it doesn't come with sounds or tutors and it was created many years ago, so some words or expressions taught are rather strange.

A computer program teaching Esperanto can be found here. It teaches grammar and basic vocabulary and it contains sound files, songs, dictation exercises and the like, so it is fun to use. Tutors are available, too. A disadvantage of this course is that it never goes beyond the sentence level - texts would help seeing words in action better.

"Jen nia mondo" is a Pimsleur-like audio-only course, which you could use in your car for example. Unfortunately this one is not available for free, you have to buy the CDs.

If you want a really quick introduction to Esperanto in just 2 hours or so, have a look at this quick and dirty guide or these lessons.

Esperanto, like any language, doesn't lack in vulgar words for swearing and the like. If you enjoy learning those, you could do an Esperanto grammar course based on swearing and sexual words.

Some people have been able to learn Esperanto by immediately diving into the language and reading original materials, but normally it is recommended that you at least have some basic knowledge of Esperanto grammar before you do so. Once you're ready, a good way to start is to read Lernu's Library or to participate in Esperanto forums and chats. Texts and forums on the Lernu site have the advantage that you can hover over any word to see its translation or definition, that way reading even 30% unknown texts is doable. You could also read the novels "Gerda malaperis" or "Fajron sentas mi interne", both of which were written originally in Esperanto and use rather easy language. There's also a comic strip in easy Esperanto.

As a course for intermediate or advanced students who seek to further improve their language, the book "Vojaĝo en Esperanto-lando" by Boris Kolker is the way to go. Along with vocabulary and expression, it teaches Esperanto culture, for example by introducing you to famous poets who wrote in Esperanto.

You will be amazed at how many more Esperanto courses you can find, both online and in print. Esperanto is probably the language best represented on the internet in that respect. So take your pick and get started!