Pre Shavuot belief check
I started reading Professor Menachem(Marc) Kellner's book Dogma in Medieval Jewish Thought..(I have not yet read Marc Shapiro's book on the 13 principles of faith). He states that Torah and Rabbinic Judaism actually was pretty dogma free. It was much more concerned with actions rather than beliefs. Dogma was introduced first by Saadya Gaon in Emunot v'Deot as a response to the challenges of other faiths, mainly Karaiites and Islam. Other religions(including Christianity) had been considered Avoda Zara and therefore did not pose a theological threat. It was only the rise of monotheistic beliefs with a defined theology that required a Jewish response in kind. Obviously, Rambam(Maimonides) further catagorized and classified Jewish beliefs into his famous 13 principles.
The Mishna in Sanhedrin discusses people who have no part in the next world. As Prof. Kellner puts it, dogma is neccessary only to define who is part of the group, and who will achieve salvation(however you want to define salvation). He posits that the Mishna that discusses those who do not have a part in the world to come really doesn't constitute dogma, because many of the things that make one inelgible are actions, not beliefs. I would add that the use of the word "says"(as in " one who says....") may reflect an action as well, and may not apply to a privately held(and unspoken) belief.(I have not looked up the gemara in a while, so I may be wrong, feel free to correct).
Prof. Kellner holds that Judaism was more concerned with "belief in" rather than "belief that". If you think about the Ten Commandments, the first is "I am the Lord Your God." It is a statement, not a command, like "keep Shabbat" or "you may have no other gods." According to this, we are obliged to have belief in God, and follow His dictates, not neccessarily to believe a whole list of things about God. An analogy can be made to an earthly king or government(lehavdil). It is sufficient to accept the rule of the governement and keep the laws. One doesn't neccessarily have to believe all sorts of other things about the government.
However, Prof. Kellner doesn't address the command of v'ahavta, you should love God. That wouldn't be a belief, but a state of mind, something else entirely. Food for thought, to go along with the blintzes.
PS. R. Gil Student references a critique and Charles adds historical context in the comments.