The games do not start
The multi-player games require functional Java. Download Java from http://www.java.com/en/ and install it. Afterwards, you should activate the check "Use Java" under Start -> Settings -> Chat on spinchat.com.
If games only do not work occasionally, it may help if you delete the Java cache and de-activate it permanently. In Windows, this can be done in the control panes of windows under "Java". You will find the instructions along with screenshots on how to find the Java control panel here (german only!).
The games "during your break" require functional flash. You can download Flash here.