>Does that really happen enough to worry about?
Yes, of course it does. There are literally millions of violent crimes in the US in any given year.
>Should I spend my money on a newer, safer car or a gun?
I leave that to you to decide. I don't know you. Bringing a gun into your home might make you less safe if you are an irresponsible person or if you have psychological issues. If you are a responsible person with no psychological issues, but you live in an area that has virtually no violent crime, then it might just be a waste of money.
>I can't imagine that there are that many scenarios where a gun saves the day from violence
There are estimated to be over 100,000 defensive uses of guns in the US each year. The widespread ownership of guns has had a clear influence on the behavior of violent criminals. Particularly, in the US, criminals avoid breaking into homes when they are occupied, because they know many occupants will be armed.