We hear a lot about gun violence, mostly because it's always in the news, but just because a day doesn't go by without it, doesn't mean the average American should be worried about it. CNN says about 8,000 people get bit by rattlesnakes a year, but it would be unfair to suggest everyone should be worried when in fact only people in a few places really need to worry. The same applies to gun violence, most of America is quite safe. As an example here is a map of the area around Chicago showing where the last 400+ murders happened. As you can see if you don't spend time in their "war zone", you have very little to worry about.
Gun death deaths in America:
11,208 homicides, including 987 that were killed by police last year
505 deaths due to accidental or negligent discharge of a firearm,
281 deaths due to firearms use with "undetermined intent".
Of the 2,596,993 total deaths in the US in 2013, 1.3% were related to firearms.
Most laws try to reduce the violent crime by controlling tools which are available all over the US but are only used by violent criminals in tiny parts of the US. The least used firearms for violent purposes are Assault Weapons, which according to Barbara Boxer, (who hates guns), only account for 2% of the gun deaths. I wouldn't guess that from what I see in the news.