The major are
Orthodox
Conservative
Reform
There is Modern Orthodox, which is abiding the laws of the Torah while still living in the current, secular world.
Conservative is deliberately non-fundementalist, less strict, but still upholds many of the laws.
Reform is the least strict.
Going off from Orthodox, there are Chassidic groups, who came off from the teachings of Baal Shem Tov, often seen as the 'father of Hasidim". He passed it on to the Maggid(Reb. Dov Ber Friedman), and then broke off into many different Hasidic dynasties, such as Chabad, Breslov, Carlebach, etc.
Chassids usually live in Chassidic comunities, and uphold the laws very strictly. They are more insular than Modern Orthodox Jews.
Chassidic Judaism is also more 'mystical' (I guess), many with their own books about Kabbalah (real Kabbalah, not Madonna + hollywood's Kabbalah), such as the Tanya (Chabad).
There is also Reconstructionist Judaism, but I know very little about that, so here's a link (I know wikipedia is not the most reliable, but it gives the gist): http://en.wikipedia.org/wiki/Reconstructionist_Judaism