Star Wars Episode 1:
The Phantom Menace

The Hunting of the Jedi

We now know that Anakin Skywalker has met Yoda, and from Ben's admission in Return of the Jedi that he (Vader/Anakin) knew Obi-Wan. Additionally, Senator Palpatine has met Obi-Wan. However, in Star Wars, Grand Moff Tarkin insisted to Vader that "you my friend are all that's left of their old religion" (or some such line).

Presumably Palpatine and Vader are directly responsible for the near-extinction of the Jedi, yet neither Palpatine nor Vader seem to care that Obi-Wan and Yoda are still alive! Since it is unlikely that they would have forgotten about them, there are only two possibilities:

1. They believe them to have died of old age. This is plausible in Obi-Wan's case, but less so for Yoda. It is unlikely that Yoda ever would have had reason to tell Anakin the normal lifespan of his species.
2. They believe them to have been killed. This may mean that both Yoda and Obi-Wan faked their own deaths, in order to wait for Luke or Leia to awaken to their latent Jedi talents. However, Leia certainly knew that Obi-Wan might still be alive (why send a message to someone known to be dead?), so it is not unreasonable to believe that others would know this as well.

The twins, Luke and Leia

It is unclear whether Obi-Wan took Luke to Owen Lars with Anakin's consent. Obi-Wan told Luke that he kept Anakin's lightsaber with Anakin's permission, but Obi-Wan has lied to Luke in the past. It is possible that Obi-Wan abducted Luke (and stole Anakin's lightsaber) once he knew Anakin had crossed to the Dark Side. The reason for concealing Leia's existence from Anakin is unclear. Anakin knew that his wife (presumably Amidala) gave birth to Luke, but did not know that Leia had been born as well. Either Anakin did not know that she was carrying twins, or there was a conspiracy to prevent Anakin from knowing. In Return of the Jedi, Luke asks Leia what she remembers about her mother. Leia replies that she only had some impressions, and Luke in turn says that he has no memory of his mother. If taken at face value, this implies that Luke was the one separated from his mother at birth, and that Leia remained with Amidala for some time. More likely is that Leia's impressions are not of Amidala, but rather her adopted mother on Alderaan.

Anakin's Fall

It may be too soon to speculate on why Anakin turned to the Dark Side. In the novelization of the movie, Yoda says that Anakin's fear is for the loss of his mother. It is likeliest that Anakin is turned as a direct consequence of his mother's death. Anger is said to be the emotion that leads to the Dark Side the easiest. If Shmi were murdered, then the anger and vengeance kindled in Anakin could turn him to the Dark Side. Is it conceivable that Palpatine himself murdered Shmi so as to gain his new apprentice? If so, there are two possibilities: Anakin did not know who killed his mother, and in his rage, turned to the Dark Side and was "captured" by Palpatine. Alternatively, Anakin did know Palpatine was his mother's killer (or had her killed), and when his thoughts turned to revenge and the Dark Side, Palpatine used his superior Dark Side abilities and made Anakin his apprentice.