Seeing some of the atrocities going on in the world right now, I have some sympathy with Light's idea: if he gets rid of the evil people then he'll get rid of the evil. But like others have said, I don't think it would work. We all have at least some capacity for doing wrong, so a world with humans in it can never be perfect. Just as Light has to keep on killing, it'd never end. Plus he ends up killing innocent people to hide his secret. Would you do that too? Which crimes would be 'bad' enough to punish with death? Where would it end?
So, though it may be tempting, I wouldn't do it. I think the guilt would destroy me, and if not, the power would drive me crazy. Just look how Light ended up!
As for the 'smaller evils', the death note would only save the victim if you somehow knew the attacker's name as well as their face, and you could quickly write it in. By that time it'd probably be too late to stop the attack, and it comes back to whether you think you have the right to kill criminals. I wouldn't want that responsibility.
Thankfully, I'm pretty sure Shinigami don't exist, so they shouldn't be dropping death notes to Earth anytime soon 