Thanks for all the Hints. Using Tomcat8 I also added a filter like @Jasper de Vries wrote. But in the newer Tomcats nowadays there is a filter already implemented that can be used resp just uncommented in the Tomcat web.xml:
<filter>
<filter-name>setCharacterEncodingFilter</filter-name>
<filter-class>org.apache.catalina.filters.SetCharacterEncodingFilter</filter-class>
<init-param>
<param-name>encoding</param-name>
<param-value>UTF-8</param-value>
</init-param>
<async-supported>true</async-supported>
</filter>
...
<filter-mapping>
<filter-name>setCharacterEncodingFilter</filter-name>
<url-pattern>/*</url-pattern>
</filter-mapping>
And like all others posted; I added the URIEncoding="UTF-8"
to the Tomcat Connector in Apache. That also helped.
Important to say, that Eclipse (if you use this) has a copy of its web.xml and overwrites the Tomcat-Settings as it was explained here: Broken UTF-8 URI Encoding in JSPs