I think I RPG'd myself out in the 16-bit era, when every friendly character death was an almost farcical hyperdrama. You just stop caring after a while (WAY TO DIE AT LVL 70 ON A NEW GAME+, CRONO). By the time I started hitting RPG's with stories I could take seriously, I think I was just inoculated against feeling sad from playing a video game.
Seriously, just get through the entirety of Tales of Phantasia, and you'll never take any sad scene in a video game seriously again. I mean it.
Which is actually weird because I'm probably too sensitive to this kind of stuff, and I cry a lot. Actually, now that I think about it, I just have a totally different relationship with video games than with other media. Sad scenes in video games are fine, but I can't watch sad movies without crying and feeling upset for hours. And I try pretty hard to avoid TV shows where things don't magically "work out" in the end because they leave me feeling bad. Same thing with violence. I leave the room and go do something else when my boyfriend watches an episode of Boardwalk Empire because that show is too much for me. But I can blow people up like nobody's business in video games!