I just installed and re-installed IntelliJ. Every Java file is coming up RED. I checked the JDK; it is at 1.6.##. The maven clean install build worked just fine
I was trying to use all the advices above, but unfortunately no one helped me. So finally I've decided to delete my intelij workspace and create the new one - it helped :) But earlier I was also doing cleaning the cache, reimporting maven projects, cleaning projects and rebuilding them.