I'm a Linux user, so this is my disclaimer: I don't have any problems right now. However, a LOT of Mac OSX users have reported the following problem:
"The application just bounces in the tray for a bit, and the game doesn't start. If I use the web client, it hangs after login."

This *MAY* be a problem with the Mac version of Java for 32-bit systems. What does that mean? It means that your OS may be fighting with Java because of a new java version.

I need someone who is having this problem to try the following:
1. Install OpenJDK from this link: http://openjdk-osx-build.googlecode.com/files/OpenJDK-OSX-1.7-universal-...
2. Open the Java Preferences utility (Hold Command + Shift, press the U key, select Java Preferences)
3. Move the version of Java whose author is OpenJDK (should be 7 edition) to the top
4. Try running Spiral Knights from the tray.

If this fixes it, we need to mention this to someone at OOO so they can resolve it in a future patch.