IntelliJ IDEA: add Project Files to Version Control?

Do the contents of the .idea project folder and the .iml module files belong into version control?

Yes, says the IntelliJ team:

Here is what you need to share:

• All the files under .idea directory in the project root except the workspace.xml and tasks.xml files which store user specific settings
• All the .iml module files that can be located in different module directories

No for .iml files say Maven users who are annoyed by ever-changing iml files, see these 2 older but still open bugs:

• http://youtrack.jetbrains.com/issue/IDEA-64312
• http://youtrack.jetbrains.com/issue/IDEA-79280

What are the drawbacks if I don't share these files? None, from my experience. When doing a fresh checkout of a project, IDEA asks whether I'd like to create a new project. Yes please, and all files are generated correctly. 

The only annoyance we have had at the company from time to time is when someone accidentally adds an .iml file to the VCS. There's a feature in IDEA to stop it from asking:

Settings -> Version Control -> Ignored Files

This setting has to be applied in every project separately. And thus it's not very helpful in this case. Because every new project I check out, IDEA asks me whether I want to add the .iml file to version control (one by one), and I can just tell it to stop asking:

Conclusion

For the time being we keep IDEA files out of the VCS. Our projects are usually multi-module maven, with lots of iml files. Your mileage may vary.