Pennsylvania State University offers a free online Swedish language course. You will learn, among other things, the Swedish alphabet and pronunciation, numbers, genders, plurals and some Swedish grammar. The course is designed for people with absolutely no knowledge of the language.
A free online course offered by the Stockholm School of Economics is intended for beginners and people who have just started learning Swedish. The course covers areas such as personal pronouns, common phrases, indefinite and definite forms of nouns, possessive and demonstrative pronouns, adjectives and tenses.
The website Loecsen.com offers some free online Swedish lessons. Essentially the lessons teach phrases from different contexts, including meeting, time tracking, family, numbers, learning, colors, drinks, food, direction, in case of trouble and parting.
A number of free online services allow you to get in touch with native speakers of Swedish. You will be able to learn the language from them. In exchange, you will need to offer them English lessons. The most popular such services are ConversationExchange.com and MyLanguageExchange.com.
Language teacher Bjorn Engdahl offers his own Swedish course for free to anyone interested. The course consists of seven lessons, covering topics such as nouns, adjectives, verbs, adverbs and tenses. A "final test," also free, checks how well you learned the material.