Am I one of the only people who really likes Clara's backstory? We may not know why there are three of her but modern day Clara has really been explored in great depth in every episode IMHO. In Bells, we learn that she's looking after the two children because they lost their mum and she doesn't want to run away from them, despite the fact that she has clearly wanted to travel from a young age and that's the main reasoning behind her travelling with the Doctor, she wants to travel and because he has a time machine, she doesn't have to leave the kids.
Take this one step further in RIngs where we learn about her family background and how big an effect her mum's death has had on her and how this has almost certainly influenced the way she looks after the kids. We also see how she is refusing to be a replacement for anyone (potentially a sign from the writing that this won't be like Martha and Rose?).
Then, in Cold War, we see how she clearly wants to prove herself to the Doctor, as all new companions do, and in her scenes with the professor, we see how shaken she is by the soldiers being ripped apart. This is a real companion dilemma, as a companion, she feels like she's succeeding but then she's shot down to earth by these deaths that shake her to her core.
Then again, in Hide, she feels the same way as Rose does in End of the World. She doesn't feel like she can completely trust the Doctor and when she sees the entire life cycle of Earth, she questions whether the Doctor can even see individuals when he lives the life he does.
And then finally in Journey, we see everything come to a head between them, their distrust of each other reaches boiling but even after she forgets his name and the whole mystery thing, she still has the residual memory to trust the Doctor and wants to travel with him.
For me, the scene between them on the cliff edge before they jump is the highlight of the episode. The Doctor is desperate to know the truth behind Clara, stretched to his limit and she's terrified and confused by him. But then, despite that, they hug and it's clear that they really deeply care about each other and they're both confused by the other. There's a real complicated mess of emotions between them and I think it's good that it's not all spelled out in black and white between them like it was with say Donna where it was clear they were best friends and made obvious in Partners of Crime (not a criticism of Donna or RTD, just saying it makes a nice change).