Well, nowadays I very rarely lose a save file, almost never, in fact. So if it does happen I tend to just get pretty annoyed, then calm down and leave the game for a while, coming back to it later and simply starting again after maybe a week or two.
In the past, though, I used to lose save files quite a bit, purely because my brother tended to delete my files out of spite if we'd been arguing, or by accident when playing on the same console. We have a shared PS2 at home, but I'm at university now and live in a differnet city so that problem isn't exactly a problem now. Back when it was, I usually dealt with the problem by flying off the handle at my brother, causing him physical pain if he'd done it deliberately (which was usually the case), then starting a new game.
Nowadays, as I say, it's no longer a problem. When I'm home for holidays we tend to play different games, so neither of us accidentally deletes anyone's save file, and we usually share a file on sandbox and casual games (the only ones that we both like to play). He's grown out of deleting my files out of spite, thank God. As for my mum's Wii, or my Xbox 360, we have different accounts. I don't mind him playing on my Xbox, provided he only uses his own Gamer profile, if he ever uses mine without permission then violence will ensue (but he's smart enough and sensible enough not to do that). So that's enough to ensure our save files are kept seperate and nothing gets deleted by accident

.