I am getting errors and warnings in the log and it does not work for me either:
2017-07-01 15:35:09.444 [ERROR] [org.openhab.io.dropbox ] - [org.openhab.io.dropbox(258)] Error during instantiation of the implementation object
java.lang.NoClassDefFoundError: Could not initialize class org.openhab.io.dropbox.internal.DropboxSynchronizer
at sun.reflect.NativeConstructorAccessorImpl.newInstance0(Native Method)[:1.8.0_121]
at sun.reflect.NativeConstructorAccessorImpl.newInstance(NativeConstructorAccessorImpl.java:62)[:1.8.0_121]
at sun.reflect.DelegatingConstructorAccessorImpl.newInstance(DelegatingConstructorAccessorImpl.java:45)[:1.8.0_121]
at java.lang.reflect.Constructor.newInstance(Constructor.java:423)[:1.8.0_121]
at java.lang.Class.newInstance(Class.java:442)[:1.8.0_121]
at org.apache.felix.scr.impl.manager.SingleComponentManager.createImplementationObject(SingleComponentManager.java:236)[31:org.apache.felix.scr:2.0.6]
at org.apache.felix.scr.impl.manager.SingleComponentManager.createComponent(SingleComponentManager.java:108)[31:org.apache.felix.scr:2.0.6]
at org.apache.felix.scr.impl.manager.SingleComponentManager.getService(SingleComponentManager.java:906)[31:org.apache.felix.scr:2.0.6]
at org.apache.felix.scr.impl.manager.SingleComponentManager.getServiceInternal(SingleComponentManager.java:879)[31:org.apache.felix.scr:2.0.6]
at org.apache.felix.scr.impl.manager.SingleComponentManager.getService(SingleComponentManager.java:823)[31:org.apache.felix.scr:2.0.6]
at org.eclipse.osgi.internal.serviceregistry.ServiceFactoryUse$1.run(ServiceFactoryUse.java:212)[org.eclipse.osgi-3.10.101.v20150820-1432.jar:]
at java.security.AccessController.doPrivileged(Native Method)[:1.8.0_121]
at org.eclipse.osgi.internal.serviceregistry.ServiceFactoryUse.factoryGetService(ServiceFactoryUse.java:210)[org.eclipse.osgi-3.10.101.v20150820-1432.jar:]
at org.eclipse.osgi.internal.serviceregistry.ServiceFactoryUse.getService(ServiceFactoryUse.java:111)[org.eclipse.osgi-3.10.101.v20150820-1432.jar:]
at org.eclipse.osgi.internal.serviceregistry.ServiceConsumer$2.getService(ServiceConsumer.java:45)[org.eclipse.osgi-3.10.101.v20150820-1432.jar:]
at org.eclipse.osgi.internal.serviceregistry.ServiceRegistrationImpl.getService(ServiceRegistrationImpl.java:496)[org.eclipse.osgi-3.10.101.v20150820-1432.jar:]
at org.eclipse.osgi.internal.serviceregistry.ServiceRegistry.getService(ServiceRegistry.java:461)[org.eclipse.osgi-3.10.101.v20150820-1432.jar:]
at org.eclipse.osgi.internal.framework.BundleContextImpl.getService(BundleContextImpl.java:619)[org.eclipse.osgi-3.10.101.v20150820-1432.jar:]
at org.apache.felix.cm.impl.helper.BaseTracker.getRealService(BaseTracker.java:205)[3:org.apache.felix.configadmin:1.8.12]
at org.apache.felix.cm.impl.helper.ManagedServiceTracker.updateService(ManagedServiceTracker.java:102)[3:org.apache.felix.configadmin:1.8.12]
at org.apache.felix.cm.impl.helper.ManagedServiceTracker.provideConfiguration(ManagedServiceTracker.java:85)[3:org.apache.felix.configadmin:1.8.12]
at org.apache.felix.cm.impl.ConfigurationManager$UpdateConfiguration.run(ConfigurationManager.java:1772)[3:org.apache.felix.configadmin:1.8.12]
at org.apache.felix.cm.impl.UpdateThread.run0(UpdateThread.java:141)[3:org.apache.felix.configadmin:1.8.12]
at org.apache.felix.cm.impl.UpdateThread.run(UpdateThread.java:109)[3:org.apache.felix.configadmin:1.8.12]
at java.lang.Thread.run(Thread.java:745)[:1.8.0_121]
2017-07-01 15:35:09.454 [WARN ] [org.openhab.io.dropbox ] - FrameworkEvent WARNING - org.openhab.io.dropbox
org.osgi.framework.ServiceException: org.apache.felix.scr.impl.manager.SingleComponentManager.getService() returned a null service object
at org.eclipse.osgi.internal.serviceregistry.ServiceFactoryUse.factoryGetService(ServiceFactoryUse.java:232)[org.eclipse.osgi-3.10.101.v20150820-1432.jar:]
at org.eclipse.osgi.internal.serviceregistry.ServiceFactoryUse.getService(ServiceFactoryUse.java:111)[org.eclipse.osgi-3.10.101.v20150820-1432.jar:]
at org.eclipse.osgi.internal.serviceregistry.ServiceConsumer$2.getService(ServiceConsumer.java:45)[org.eclipse.osgi-3.10.101.v20150820-1432.jar:]
at org.eclipse.osgi.internal.serviceregistry.ServiceRegistrationImpl.getService(ServiceRegistrationImpl.java:496)[org.eclipse.osgi-3.10.101.v20150820-1432.jar:]
at org.eclipse.osgi.internal.serviceregistry.ServiceRegistry.getService(ServiceRegistry.java:461)[org.eclipse.osgi-3.10.101.v20150820-1432.jar:]
at org.eclipse.osgi.internal.framework.BundleContextImpl.getService(BundleContextImpl.java:619)[org.eclipse.osgi-3.10.101.v20150820-1432.jar:]
at org.apache.felix.cm.impl.helper.BaseTracker.getRealService(BaseTracker.java:205)[3:org.apache.felix.configadmin:1.8.12]
at org.apache.felix.cm.impl.helper.ManagedServiceTracker.updateService(ManagedServiceTracker.java:102)[3:org.apache.felix.configadmin:1.8.12]
at org.apache.felix.cm.impl.helper.ManagedServiceTracker.provideConfiguration(ManagedServiceTracker.java:85)[3:org.apache.felix.configadmin:1.8.12]
at org.apache.felix.cm.impl.ConfigurationManager$UpdateConfiguration.run(ConfigurationManager.java:1772)[3:org.apache.felix.configadmin:1.8.12]
at org.apache.felix.cm.impl.UpdateThread.run0(UpdateThread.java:141)[3:org.apache.felix.configadmin:1.8.12]
at org.apache.felix.cm.impl.UpdateThread.run(UpdateThread.java:109)[3:org.apache.felix.configadmin:1.8.12]
at java.lang.Thread.run(Thread.java:745)[:1.8.0_121]