First, there's Morgan, the man who saves Rick's fresh-out-of-a-coma ass. Morgan has the chance to shoot his undead wife, but just can't bring himself to do it. We later find out that Morgan's zombie wife tried to eat their kid, leaving him no choice but to finally kill her.
In Season 2, otherwise known as the season when AMC's dramatically reduced budget forced Rick and company to stay on a farm for an entire year, we are introduced to Hershel, who, unbeknownst to Rick's crew, is keeping a barn full of his zombified family members, because he can't bring himself to dispose of them.
And we all remember how that turns out.
When we are introduced to the sinister Governor in Season 3, we are led to believe he has a deep, dark secret, only to discover that it's the same damn plot point from the previous two seasons: he has a zombie daughter that he's keeping alive.
At least he's fatherly enough to use Pantene for zombies.