The word "Jew" originates from the name of the eldest son of Jacob. The term "Jew" was introduced many generations and decades after him. I wonder whether Adam, Noah, Lot, Abraham and Moses were all Jews?
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The term "Jew" is relatively recent. The Hebrew form of it ("Yehudi") first appears (I believe) in Megillas Esther and in Zechariah. Before that, Jews were referred to as "Ivrim" or "(B'nei) Yisrael" (The Children of Israel). (Thanks @IsaacMoses, for bringing up @Menachem's excellent links. I'd like to reemphasize that those should really be checked out, especially the Chabad.org one on the origin of the term "Jew".)
I'll use the word "Jew" hereinafter because it's convenient, but remember that I'm talking about the people, not the name.
Generally, Avraham (Abraham) is considered to be the first of what we now call Jews. We actually have an interesting discussion here on when he became so, and what made that happen.
Traditionally, we do not call Adam, Noah, or Lot Jews. Only from Avraham and down do we start to refer to people as Jewish.
That's not to say that Adam and Noah* weren't holy people, just that they didn't have that same special status that G-d gave to Avraham and his children. But don't worry about them, they've got their own unique places in Jewish history. (Adam, the first man, the archetype of humanity. Noah, the only worthwhile guy in the universe at the time.)
*Noah's relative holiness is disputed by the rabbinic commentators. Some say he was only considered righteous compared to the rest of his (really evil) generation, while others say he was indeed righteous by any standard. I have intentionally left out Lot, as Jewish tradition does not consider him to be much of a holy guy at all, as far as I know.)