Rewatching "The Name of the Doctor", and I still haven't figured out how Clara saves the Doctor. The Great Intelligence walks in to the Doctor's time stream and with his knowledge of the Doctor's life to turn all his victories in to defeats. Then Clara walks in after the GI and somehow her presence corrects everything. How? It's never explained and it doesn't make any sense. Did she just nullify the GI? If so how? Clara lost her memory when she was shattered in to millions of copies. The GI retained his.
Watching the two episodes that featured Clara before she became a companion proper; Asylum of the Daleks and The Snowmen. Clara's presence didn't thwart anything. Remove her from both episodes and there isn't much threat to the Doctor's life that she saves him from. The scenes with Clara edited in to clips of the Doctor's previous lives also don't affirm any contribution of her saving the Doctor.