There are certainly at least as many variants of Jews who are not fundamentalists.  Probably more.  I find it hard to identify entirely with any of them as there are so few of me around.  I am a person who knows and loves aspects of the religious world as well as of the left wing secular world.  Mostly, I find myself resisting any rigid ideology.
Among non-fundamentalists, who still see themselves as relgious, there are Reform, Conservative and Reconstructionist as well as other movements. They are all attached to their particular way of being Jewish, ways which are more typical of the Diaspora than of Israel.   In brief, Reform Jews do not believe that the law is eternal in all its aspects.  The Tanakh and Talmud were written by people who were inspired and wanted to transmit the Divine but they were obviously influenced by the culture of the times in which they wrote.  They give much more importance to the ethical parts of the law and those writings that govern relationships with other human beings.  They are more attached to the Prophets and to Psalms than they are to Leviticus, for
example.  They see things like eating Kosher as optional for Jews, not obligatory although they still all hold with male circumcision.  However, many Reform Temples will continue to serve Kosher food at their functions to try to preserve the unity of the Jewish people.  Unlike fundamentalist
prayer services, reform services do not include a prayer for the rebuilding of the temple since they see the time for the temple as past.  The Reform movement at first rejected the concept of the messiah although I am not sure where they are on this now.  Similarly they were at first anti-Zionist but
have become increasingly supportive of Israel over the years, especially since the 6 day war of 1967.  This is the largest movement in the United States and the smallest of the big 3 in Canada.  Many will have links to left wing movements in Israel.
Conservatives are an odd mix of fundamentalism and reform.  One can think of them as people who like tradition but in their daily lives are not at all fundamentalist.  They are the movement which has the greatest difficulty in enunciating a common position on Gay marriage or on many other of the
contentious issues.  Their usual position is both yes and no.  Younger people in the movement are usually more liberal, older people more traditional but there are exceptions.  A number of egalitarian Conservative congregations have been established which foster the total equality of men and women in all aspects of the service.  Some Conservatives will follow
Orthodox practice on kashruth but most are people who will eat kosher at home but not in a restaurant.  They will drive to synagogue but only if they do not live close enough to walk.  This is the largest movement in Canada and the second largest in the States.  They tend to be strong reflexive
supporters of Israel.

In this context, I should mention the Modern Orthodox movement which had much in common with the traditional wing of the Conservative movement.  But as things become politicized in these movements, people will no doubt be
called on to “declare” where they stand.  Modern Orthodox tend to be similar to fundamentalists in many practices, eg. Wearing of kipas by males, eating kosher everywhere although being willing to take a salad in a non-kosher
restaurant.  Some of these are “koshetarians”, people who eat vegetarian everywhere and thus avoid the questions of kashruth relating to animals, birds and fish.  They often go to more fundamentalist synagogues and are considered to be a shrinking part of the Orthodox movement.  They also tend
to be strong supporters of Israel.  
Reconstructionists are an off-shoot of the Conservative movement.  They view Judaism not as a religion in the Christian sense but as a Civilization.  As members of a civilization with a long history, local Jewish communities are
called upon to “reconstruct” a Jewish life in their milieu in a way that is meaningful to them.  They choose the aspects of Jewish civilization that make most sense in the place where they live.  As you can imagine, actual Reconstructionist congregations will look very different from each other,
depending on the make-up of the congregation, some looking almost orthodox in liturgy others looking like a Unitarian service.  As they tend to put emphasis on the direct connection between Jewish communities and tradition,
they have varying degrees of connection to Israel.  Often they are connected to left wing movements in Israel.  It is the smallest of the movements.
There is a new movement originating in the States called the Jewish Renewal Movement.  It appears to be the left wing equivalent of the Chasidic movement.  It strongly emphasizes spirituality, often talks of Jesus as the Rebbe from Nazareth and has many links to Buddhism and New Age.  It is still
evolving and has drawn enthusiasts from many streams of Judaism.  
There are Secular Jews who really attend no synagogue but sometimes participate in Jewish cultural events or religious events with a strong cultural component (Chanukah, Passover, Purim, Israel Independence Day). This is a growing segment of Jewish population in North America and is
actually the largest group in Israel.  They can vary all over the map politically but the majority are left leaning, a large minority being right leaning and nationalist.
Among these, there are sub-groups such as “Jewish Humanists”, Yiddishists and Jewish communists.  These are of course overwhelmingly left wing.
In these latter groups, one can find vocal Jewish opponents of Israel and of the Jewish religion who make common cause with Palestinians.  It is the oddest thing in the world for me to see these Jewish secularists cozying up to the Ultra-Orthodox opponents of Israel in international conferences.
Their personal philosophies could not be more different!
The Orthodox movement is the home of the fundamentalists I described in the previous article.  I would only add that fundamentalists are also divided in themselves among those who follow the Yeshiva movement (Mitnagdim) and those
who follow a charismatic leader called a “Rebbe” (Chasidim). Each Chasidic group has its own Rebbe.  These divisions could take up a book to describe.