How can I create a "modern looking" Java desktop application?

I can also offer you a new LaF to look into - WebLaF. I'am currently working on it to bring a lot of UI features and make work with Swing much easier for anyone by just using WebLaF library basic features.

A few examples showing how some of WebLaF components look like:

Some of main goals i am targeting:

1. Great and modern-looking L&F with support for all Swing components
2. An extensive set of additional components which you won't find in standard Swing
3. A big set of Utility classes to assist you with writing the code

WebLaF library also suggests a few other advantages and unique features:

1. It is an open-source project (GPLv3 licensed)
2. Easy components styling using painters system (specifically with 9-patch files)
3. Quick and easy customization of the default "Web" style
4. Lots of features to accelerate and simplify Swing application interface creation

You can try the demo-app to see if it is modern and simple enough :)

Have you looked into JavaFX 2.0? It is designed to interop easily with Swing, and has many modern 'good looking' controls.

Also, as lrAndroid mentions, a Swing app can look like a native app if you set the system look and feel with:

UIManager.setLookAndFeel(UIManager.getSystemLookAndFeelClassName());

Look into changing the Look and Feel of your Java program. This allows you to customize the overall "theme" of your program.Here is information on changing the LAF.