The University of Pennsylvania supports a comprehensive website for learning Tamil called WALTT--Web-assisted Learning and Teaching of Tamil. The site offers lessons in three units, broken up into Beginning, Intermediate and Advanced. The beginner's level starts with the alphabet, including how to write it in Tamil's unique script, then moves on to vocabulary, tense formation and conversational exchanges. There is also a listening test.
The intermediate level adds more emphasis on reading and writing in Tamil, with writing projects, jokes, a Tamil reader, a cloze (fill in the blank) quiz and more comprehension tests. The advanced level is even more complex, giving the student short novels, radio plays, short stories, video and songs in Tamil. There is even a "Miscellaneous" section to download software, including "Tamil A to Z" for Mac, look at pictures relating to Tamil culture, download Tamil fonts and learn how to make Web pages in Tamil Unicode.
Another website filled with Tamil learning materials is Thamil Paadanol-Learn Tamil, written by Elango Cheran. Twelve chapters cover a wide spectrum of information about Tamil. The first few chapters alone include lessons on the alphabet, pronunciation, verb roots, numbers, time, colors, questions words, adverbs and adjectives. Things get more complicated as you go up through infinitives, verb tenses, passive voice, negative statements and complex sentences. There are also appendixes with more verbs, seasons and months, and advanced numbers, and a links page with even more resources about Tamil.
Learn Tamil Through English also features a great number of resources for learning Tamil, offering all the information on PDF files. There are 25 grammar lessons covering various aspects of verbs, tenses and nouns, and special sections with stories, songs, movie dialogues and household words. There is also a PDF file of class lessons, which include student exercises. Everything is done in Tamil script, so you are not dependent on English transliteration. You can also take quizzes and tests to prove your comprehension. You can download each PDF separately, or get all the information in one zip file.