Which is correct: "So far as I know" or "As far as I know"?

Solution 1:

Both are equally valid because as far as and so far as have exactly the same meaning in this context. However, so far as may be considered a slightly less formal version of in so far as.

as far as
to the extent that:
as far as I am concerned, it is no big deal

(in) so far as
to the extent that:
it was a windless storm so far as blizzards go

_NOAD

However, you will likely more often hear as far as I know in casual conversation. For the extremely formal, in so far as I/we know would not be out of place.

Solution 2:

"As far as I know" is the idiomatic expression I'm familiar with.

as far as conj. To the degree or extent that: They returned at nine, as far as we know. Usage Note: As far as the Usage Panel is concerned, as far as had better be followed by both a subject and a form of go or be concerned. As far as is sometimes used as a preposition meaning "as for" or "regarding," especially in speech, but a large majority of the Panel frowns upon this usage. Eighty percent find the as far as construction in this sentence unacceptable: As far as something to do on the weekend, we didn't even have miniature golf. Eighty-four percent reject the sentence The Yankees are still very much alive, as far as the divisional race. Further, 89 percent object to as far as when followed by a noun clause, as in As far as how Koresh got shot, we don't know yet.

_{[The American Heritage® Dictionary of the English Language, Fourth Edition copyright ©2000 by Houghton Mifflin Company. Updated in 2009]}

According to the same source "so far as" is a variation of "insofar as" :

so far as conj. Insofar as: So far as I am concerned, the project is over.