The Washington Post carries a very babyish and silly article, “Judaism without God? Yes, say American atheists,” timed to the upcoming Jewish high holy days. It’s a spin on the old “Have your cake and eat it too” theme that we’re familiar with from the discussion with theistic evolutionists. Excerpt:

Unlike other religions, Judaism has often embraced its atheist strain. The 18th-century Dutch philosopher Baruch Spinoza was excommunicated from his Jewish community for equating God with nature. Today, his writings are studied by many Jews.
In the 1920s, American Conservative Rabbi Mordecai Kaplan developed the theology of what would become Reconstructionist Judaism, founded on the idea that God is not personal, but a summation of all natural processes. Four decades later, Reform Rabbi Sherwin Wine came out as an atheist and founded “Humanistic Judaism,” which emphasizes secular Jewish culture and history over belief in God.
And because Judaism is not dogmatic — unlike Christianity and Islam, there is no creed to adhere to — atheists can be open about their lack of belief and still belong to a synagogue.

The article is full of simplistic, ill-informed and thumb-sucking clich�s, as I trust many non-Jewish readers will be able to detect. As to the substantive question that’s raised in the headline, it comes up often enough that I thought, despite being slightly off topic, it would be interesting to bring up here.
You have distinguish Judaism, a faith, from the identity of being a Jew, in the sense of belonging to a group of people related by biological family ties and to whom the faith called Judaism was entrusted by God.
Just as in an ordinary family unit, rejecting or distorting your family’s inherited beliefs and values, casting off the family name and even reviling your parents and siblings doesn’t mean you cease to belong to your family — so too with Jews and Judaism. Rejecting authentic Jewish belief in favor of atheism or whatever you like may mean you’re an alienated Jew, a lost Jew, or nowadays more likely an illiterate, incurious and ignorant Jew, but you’re no less a member of the Jewish people for all that.
There’s a symposium on this same question, just out in the Jewish magazine Moment and referred to in the article, that I contributed to. It was a telephone interview so not as articulate as I’d like, but this is how they quote me in answer to the question, “Can There Be Judaism Without Belief in God?”

It depends on what you mean by Judaism.
In the Guide for the Perplexed, Maimonides talks about words that mean different things in different contexts. There are different meanings for words when they are used in reference to God and when they’re used in reference to people, like “sit” or “stand.” So you have all kinds of philosophies that go by the name Judaism. If you consider Judaism to be what people of Jewish background believe, I’d say, sure, you certainly can have a Jewish person who doesn’t believe in God. But there’s no way to conceive of thousands of years of historical Judaism without a deity, a designer, an ultimate, transcendent truth.
I’ve known a lot of people who do not believe in God who have come to Judaism for other reasons, such as a relationship or a philosophical view that drew them in. One of the strange and miraculous things about Jewish practice is that it seems to engender belief. People wonder, “Why does Chabad ask passersby to put on tefillin?” It seems that there’s this almost magical effect to it. The mitzvah not only provokes spiritual questions, but engenders a longing for belief, and ultimately belief itself. So even though, theologically, Judaism without God doesn’t make sense, I would say that, as a practice, Judaism can begin in non-belief but conclude in belief. For me, authenticity means truth. It means connecting with a revelation that happened in the past. If there’s any hope for Judaism at all, it lies in the belief that Judaism goes back to Moses and Mount Sinai. Otherwise, Judaism is just a fraud, an illusion.