My primary issue with them is that they eat most of the produce out of our garden (especially tomatoes; the second there's any red on them at all, they take them). They will also nest in the house if they can make a way in, though that has only happened once (to my knowledge) so far.

In moderation squirrels aren't bad at all. I am quite fond of them, actually. Around my house, though, their population was outrageous. To put it into perspective, I have taken around 50 just out of my yard over the last 2 years and there are still at least a dozen just directly around my house, without needing to even go into the woods or the other yards in the neighborhood. I am fine with this population, though, as they are no longer a nuisance so I only cull to keep the population in check anymore.

Edit: Sorry, forgot to answer your other questions. Yeah, I use a pellet gun to take them. They make a surprisingly gelatinous stock but I havent tasted it, honestly. I would expect it to be similar to chicken stock, though, judging by the smell and color. Turns to jello when you refrigerate it.