Speaking personally I can't warm to Clara at all. This means I don't actually bother if I miss an episode and that's me being a huge fan of Matt Smith's Doctor.
I like JLC a lot more than I ever liked Karen Gillan but it's hard to deny that Clara is getting only a fraction of the character development that Amy did.
She's got the usual one-liners that all of Moffat's female characters get and her main traits seem to be that unlike most Companions she actually listens to what the Doctor tells her and isn't unrealistically brave. And that's about it, really.