Orthodox, Conservative, Reform, and Reconstructionist Judaism are all based on the Talmud.

The Talmud is composed of two parts: the Mishna and the Gemara.

The Mishna is the compendium of the teachings of the Oral Torah compiled in the 2nd century CE to preserve the laws of the oral tradition. The Mishna contains the basic laws that are  the foundation of Jewish civilization, the laws by which the commandments of the Torah are put into everyday practice. The Gemara is the commentary on the Mishna that resolves contradictions between laws in the Mishna and supplies additional rules and interpretations. The Mishna and the Gemara together are the foundation of Jewish law, the laws of the Torah as interpreted by the Rabbis. All subsequent Jewish legislation is based on the Talmud.

Orthodox and Conservative Judaism consider the law system based on the Talmud to be legally binding. Reform and Reconstructionist Judaism consider them to be guides and suggestions of behavior and observance and/or the collected folkways of the Jewish people. Regardless, all major denominations of Judaism are based on the Torah as elucidated through the Talmud. If the Torah is our Constitution, the Talmud is our history of Supreme Court cases and basic law code.

There is a small population of Karaite Jews who reject the divinity of the Oral Torah and thus also the Talmud.

I'm not sure what to make of that.

By committing the Oral Torah to writing, it is true that the Oral Torah ceased to be literally "oral." it was a decision deemed necessary by the fall fo the Second Commonwealth and the increased persecution that Jews were subjected to by the Roman state.

Still, the Mishna preserved the bulk of the Oral Tradition and was supplemented later by Baraitot (elements of the Oral Torah that did not make it into the Mishna) as well as additional traditions contributed by the Rabbis of the Talmud. Also, bear in mind that there is an unbroken continuity of tradition and study from Rabbis of the Mishnaic age to today so the Oral Torah is still alive and well and is, in fact, the living and breathing soul of the Jewish religion. If the Written Torah is the body, the Oral Torah is the animating spirit.

The Mishna and Gemara were not the end fo the Oral Tradition, not by a long shot. From them is based the codes of Jewish law (such as Maimonides' Mishneh Torah and Joseph Karo's Shulchan Arukh) and the responsa literature (rabbis asking other rabbis questions on specific cases of Jewish law for research and judgment). Today's scholars across all denominations represent the latest link in the chain.