I had to spend a minute thinking about this. A few minutes, honestly. Because I can give up most of the things in my life. My upbringing wasn't terrible, not by a long shot, but it wasn't the best, either. It left me a...flexible person, I guess? That's the least cold way I can think of putting it.
So...I've gone without an internet connection for months and months at a time. Gone without other convenient methods of conversing with other people who weren't family, too, and as much as I love them, it gets tiring when you're just interacting with the same people day after day. I've dropped out of contact with all my long term friends at least once, because of the internet/phone problems or my personal things or school or what have you. My significant other is an absolutely lovely person and I love her very much, but I think I could lose that relationship, as grounding and inspiring and good for me as it is, and move on.
The thing I wouldn't give up is my fortitude, I suppose is the word. My circumstances tend to change an awful lot, that's why I'm such a flexible person, and my ability to take change in stride and try try again when it comes to roleplays or real life stuff, regardless of past failures or current problems or whatever else, is the part I most admire about myself. I mean, I have my issues with self esteem and other heavy topics along that vein. There's this certainty, though, that not matter how much right now might suck, I can always get through it, and I couldn't do without having that as something I can rely on.