For those not reading the comments before posting, please keep this one thing in mind if nothing else..... re: "but we've seen Clara's mom....."
Ah, yes we did!!!.... But did we Clara's mom pregnant with Clara???
If "yes", would someone please verify the episode and exact time during that episode for me so we can rule out this specific theory since we know Amy is Melody's mother?
If "no", please consider the possibility that Clara was either adopted by the family, or left specifically with them after careful selection, for her protection from the Doctor's enemies.
I have Part 2 of this video in the works to further detail possible connections and point out some questions that should be asked. Will link it here when it's ready!
----------------------------------------- (June 22, '13): I didn't include this in the video, but the image linked here shows perfectly why I have always thought Clara is a younger version of River...
(Note: I'm not sure who created the original Oswin/Clara split image so I'm unable to properly credit them at this time, I borrowed the Tenth/River promo image from the BBC's site, split it, re-split the Oswin/Clara image and made a new combination. Other than resizing for scale, absolutely no other alterations have been made (stretching, color etc.)... from this compilation it's easy to see that River and Clara's hair, facial structure and features are nearly 99%+ identical.)
