The Karaites are an interesting phenomenon; a breakaway sect from mainstream Judaism that once commanded a strong following, they are barely known inside the Jewish community.
It is difficult to distinguish truth from fabrication when it comes to the Karaites. Their own sources are not in agreement with normative history, while most of the rest of writing about them comes from Rabbinic sources, and can only really be described as anti-Karaite propaganda. Nevertheless, I'll try to present as accurate a picture as I can.
Origins and History
The Karaites are thought to originate with Anan ben-David in the late Eighth Century CE, in the vicinity of Babylon (modern-day Iraq). By this time, the Babylonian Talmud had been written, standardised and edited, and had begun to be distributed throughout the Jewish world. This is commonly known as the Gaonic period.
At this time, the powers and limits of Rabbinic authority were being redefined. The codification of the Talmud, while providing a huge wealth of written discussion, was also restrictive on the manoeuvrability of the Halacha. As a response to this - and to the emergence of Islam - new Jewish sects emerged in the area of Babylon. Anan united these sects around his Karaite movement. It rejected the authority the Mishnah and Talmud, and therefore all Rabbinic Judaism. Instead, it attempted to re-interpret the Torah without the Rabbis' exegesis
The Karaites themselves dispute this history. They consider themselves the descendents of the true followers of God and the Torah. They argue that these true followers were what were called the Sadducees in Roman times, and they persisted throughout the Jewish world against the publicly prominent but minority Pharisaic Rabbis. They say it was the Muslim caliphate that imposed the Talmud on all Jews. This is not considered an accurate account by most neutral historians.
In any case, all agree that Anan Ben-David organised a new anti-Rabbinic sect and was able to gain approval and recognition from the Caliph. They gradually became known as Karaites.
The mainstream Jewish response was unsurprisingly hostile, though it took some time to come to a head. There is evidence that the Karaites and Rabbis were able to co-operate in some areas, such as the codification of the Mesorah. It was Saadia Gaon who took on Karaism most explosively in the early Tenth Century. He wrote against their legal process and their customs, and essentially declared them not Jewish.
This conflict resulted in a real schism that continues, essentially, to this day. The mainstream Jewish community considers the Karaites heretics but still Jewish. As such, they can make Aliyah to Israel under the Law of Return. The Karaites themselves don't always self-define as Jewish. They were exempted from forced Jewish conscription and other anti-Jewish laws in Europe from the 18th Century. They were not considered Jews by Hitler and weren't victims of the Holocaust - though many died in the Second World War.
I've never met a Karaite, as far as I know. There are a few in the USA, some in Israel, and some still in their places of origin in Iraq, Turkey and eastern Europe. Their numbers, though, are tiny.
Laws and Customs
As a student at a Jewish school, I was always told that the Karaites - like the Sadducees - were biblical literalists, and as such behaved like morons a lot of the time: Hanging their Tzitzit on the wall, wearing their Tefillin on their noses, sat in the dark on Shabbat and pelted priests with citrons. It turns out that some of that isn't true - and some of it is.
The Karaites are not purely literalists, but they reject the Rabbis' interpretations of the Torah. They see the Rabbinic legal process as too divorced from the meaning of the text, and have their own principles for deducing meaning - and therefore laws - from the Torah. Essentially, they have their own Oral tradidion, though they claim it is sounder than the Rabbinic one.
The Karaites reject the fixing of the Jewish calendar that occurred after the demise of the Sanhedrin, and still declare the new moon every month. They determine the date for Pesach based on the barley-harvest in Israel. They follow the old Sadducee practice of holding Shavuot on a variable date which is always a Sunday.
The Karaites do have tzitzit, but they are very different from the traditional Jewish type: They are blue and white, and plaited. They don't wear tefillin, as they consider biblical references to them to be a metaphor. Karaites are sometimes egalitarian in prayer, but maintain the gender differences inherent in the Torah text (such as over divorce laws). They don't intermarry with Jews. For many centuries they would sit in the dark on Shabbat and eat cold food, following the Torah law not to have a fire in your house on Shabbat (mainstream Judaism considers that this prohibition applies only to making a new fire). Nowadays, I believe they use electrical lighting, as they don't consider it to be fire.
These are only a few examples of the differences between Karaism and mainstream Judaism. They are an interesting group of people that developed its own identity and maintained it for more than a thousand years, and shouldn't be consigned into history just yet.
http://www.jewishgates.com/file.asp?File_ID=354 - Saadia stuff
http://www.jewishgates.com/file.asp?File_ID=91 post-babylon history
http://www.karaite-korner.org/ The Karaites' own website
Wikipedia articles on Anan ben David (very anti-Karaite) and Karaites