First of all you need to take a look at where you are getting your news from. It's usually best policy to just ignore anything that Fox News and The Daily Mail have to say straight away.
If you want to talk rape it's important to know that Sweden files rape in a different way to the US and most of Europe. If a wife says that her husband raped her 75 times in the past year, that would be counted as 75 different filed reports. Whereas in most other places it would be counted as 1. This is why Sweden appears to have high rape rates. That and the fact that the public satisfaction with police is higher than any other country in Europe, meaning that more victims feel comfortable reporting their rape, unlike in the US where the majority go unreported. The newspapers love saying that in Sweden 1 in every 4 women is likely to get raped, but this number doesn't seem to be true based on the above information. Plus in the US that number is 1 in every 3. So maybe you should be focussed on the rape endemic over there.
What is happening in Germany is that right wing nazi groups are taking exception to the refugees coming into the country. As a result they are doing things like taping racist posters over walls and hiding razor blades underneath in the hopes that people who try to take them down will be hurt. These nazi groups are hosting public meetings and demonstrations. They are the biggest opposition voice.
Where I am in Scotland, UK, we have decided to accept refugees and we have had no trouble. We actually got a plane full of refugees to be placed in our city a couple of weeks ago and it turned out that the majority of them were actually Christians not Muslim. We haven't had any increased crime rates apart from one instance where someone vandalised a Muslim graveyard. So actually it seems to be the anti-refugee people causing the most trouble.
To answer your question I am not scared, I am not scared at all. And as for it happening in the US? Well Ted Cruz hurried himself to pass some legislation and is saying that the US will only accept Christian refugees (most of which are women and children), and they can apparently only accept 10,000 refugees for the entirety of 2016. So I would say that you don't have to worry about that.
Instead I recommend that you worry about the high rates of rape, shootings and domestic terrorism in the US because they are far more dangerous to you.