Human Connection
Robert hasn't seen another human being in a very long time and he hopes for such a meeting. But ironically when Anna and Ethan arrive and are staying in his home their very presence makes him uncomfortable. Though he wants connection he has lost his ability to fully trust another person as they are unpredictable and do things outside the bounds of his routine that he's been in.
Faith
Robert no longer believes in God after he has watched his family and billions of people be killed or become infected. Thus his faith is gone. Ironically it is his faith that allows him to see clearly and make the decision to protect Anna and Ethan sending them away with the antivirus as he dies killing the infected who've overrun his home. It is his faith that allows him to know that this is his last act on earth.
Cure for Cancer
We see Dr. Alice Krippin at the beginning of the film stating that she has found the cure for cancer. That every patient she has given her vaccine to has had a full recovery from the disease. Ironically her miracle drug that is curing everyone becomes the cause of a mutation that nearly wipes out all humanity of earth.
Isolation
Robert after capturing one of the infected sees his mannequin from the dvd store in the middle of the street where he should not be as he didn't move him. Robert knows deep down that the mannequin is not real and that it didn't walk it's way into the street. Ironically because of his isolation, Robert demands for the mannequin to tell him if he is real or not as he does not know the answer to that himself anymore. From this Robert is led into the trap of the infected where he is strung up by his foot. All of this eventually leads to Sam's death.
Protecting the Ones You Love
When the virus outbreak as reach a critical limit Robert takes his wife and daughter to the dock by the bridge in order to get them on a helicopter off the island. All of the city is trying to get off Manhattan and Robert has to will them on to the chopper. Ironically their getting on board is what causes them to lose their lives as another helicopter crashes into them on their way to safety.
