How to have the formatter wrap code with IntelliJ?

Do you mean that the formatter does not break long lines? Then please check:

Settings / Project Settings / Code Style / Wrapping

Update: In later versions of IntelliJ, the option can be found under:

Settings / Editor / Code Style

There select Wrap when typing reaches right margin.

IntelliJ IDEA 14, 15, 2016 & 2017

Ensure right margin is not exceeded

File > Settings > Editor > Code Style > Java > Wrapping and Braces > Ensure right margin is not exceeded
Reformat code

Code > Reformat code...

or press Ctrl + Alt + L

If you have something like this:
```
thisLineIsVeryLongAndWillBeChanged();   // comment
```
it will be converted to
```
thisLineIsVeryLongAndWillBeChanged();   
// comment  
```
instead of
```
// comment  
thisLineIsVeryLongAndWillBeChanged();   
```
This is why I select pieces of code before reformatting if the code looks like in the previous example.

IntelliJ IDEA 14: File > Settings > Editor > Code Style > Wrap when typing reaches right margin
IntelliJ IDEA 15, 2016 & 2017: File > Settings > Editor > Code Style > Wrap on typing