Feelings
Feelings are something we as humans all have, but the Doctor is a Time Lord and is very different from us. Now, there are times when the writing and the way things seems the Doctor has feelings for a companion. One time to note is with Rose. Everyone who watches the program can tell Rose is in love with the Doctor. This all ends with the half human Doctor staying with her in the parallel universe. There are also times during the Tenth Doctor’s reign that it does seem he has feelings for Rose.
During season five in Amy’s Choice, the Dream Lord talks about the Doctor having feelings for Amy. Of course, the Doctor never denies this. There is one thing I have always noticed with Doctor Who. Whoever the Doctor is, he seems to maybe has love for some companions. These feelings may not those of love or may be they are. I do have to wonder sometimes especially since the Doctor is so close to some of the companions, and I cannot say that the Doctor loves all female companions, but at times I have to wonder.
I can say that while watching the Eleventh Doctor, the stories at time seem to point to the Doctor having feelings for Amy. There are times when I actually think that the Doctor and Amy have a child. Hey, I know that is not really true, but their relationship to me shows that could have happened. Now, I do not know if Steven Moffat meant for that to an underlying theme or not. But the tension between the three was there. There are times when Amy seems to love the Doctor more than Rory. Then Rory see this and I know that he worries about this. He even approaches Amy about it.
So, my thoughts on this is that yeah, I believe the Eleventh Doctor did have feelings for Amy. But I don’t know if you can say that he loved her that way, but this may have been just like so many others. The Doctor always cares for his companions. Which means there is a possibility he does have feelings.