Did Snape ever feel any real loyalty to either side of the war?
Before his past was revealed, there had been a lot of argument about whether Snape would ultimately turn out to be good or bad, but now that we know his past, some people (including me) would say that he was neither.
Yes, he was saving Harry's life the entire time. And yes, he would do anything to help bring the destruction of the man that killed Lily. But just because he was on the good side doesn't necessarily make him good. Now, he wasn't ever Voldemort's man, nor was he Dumbledore's man. I think it's clear that he was his own man, and he just chose to do the things that would help Dumbledore's cause. But not out of loyalty to Dumbledore--it was always out of loyalty to Lily.
And I don't think that, as a nineteen year-old man that became a Death Eater, he would have considered himself entirely bad, either. His entire life, all Snape wanted to do was power, and to fit in. In a world where he was teased and hated by everyone but Lily and the other Slytherins that were aspiring to be Death Eaters, it was the easy choice, because being a Death Eater would have given him both of those things. And he made the mistake of choosing what was easy instead of what was right, which he was pushed even further into by his corrupted childhood and interest in the Dark Arts.
But that's just my opinion. Others will say that Snape would only have ever left the Death Eaters for Lily, which would have made him 'evil' at some point if not always evil, and some will say that he would consider himself good ultimately, since he did everything for the Order and saved many lives. I would disagree with both of those groups of people.
