I'm having the same problem, here is the error log:

Spine 1.0.10-trial
Windows 7 amd64 6.1
NVIDIA Corporation
GeForce GTX 260/PCIe/SSE2
3.3.0
Java 1.7.0_10
Oracle Corporation
Java HotSpot(TM) 64-Bit Server VM
Started.
Uncaught
java.lang.IllegalStateException: no splash screen available
	at java.awt.SplashScreen.checkVisible(Unknown Source)
	at java.awt.SplashScreen.close(Unknown Source)
	at com.esotericsoftware.spine.editor.Editor.render(Unknown Source)
	at com.badlogic.gdx.backends.lwjgl.LwjglCanvas$3.run(Unknown Source)
	at java.awt.event.InvocationEvent.dispatch(Unknown Source)
	at java.awt.EventQueue.dispatchEventImpl(Unknown Source)
	at java.awt.EventQueue.access$200(Unknown Source)
	at java.awt.EventQueue$3.run(Unknown Source)
	at java.awt.EventQueue$3.run(Unknown Source)
	at java.security.AccessController.doPrivileged(Native Method)
	at java.security.ProtectionDomain$1.doIntersectionPrivilege(Unknown Source)
	at java.awt.EventQueue.dispatchEvent(Unknown Source)
	at java.awt.EventDispatchThread.pumpOneEventForFilters(Unknown Source)
	at java.awt.EventDispatchThread.pumpEventsForFilter(Unknown Source)
	at java.awt.EventDispatchThread.pumpEventsForHierarchy(Unknown Source)
	at java.awt.EventDispatchThread.pumpEvents(Unknown Source)
	at java.awt.EventDispatchThread.pumpEvents(Unknown Source)
	at java.awt.EventDispatchThread.run(Unknown Source)

Does anyone know what the problem is and how I can get it working?

Hey guys, thanks for the crash reports, we will get it fixed as quick as we can. Hopefully tomorrow depending on how severe the crash is. I've managed to reproduce it, so once it's working here, we will send out another version.

Oops, sorry about that. This is fixed in 1.0.11 which is now available. We tested the hell out of 1.0.10, but of course it was one last seemingly innocent change that broke things...