Since you didn't give any details as to the version of BIRT you are using or the servlet exception logged in your web server instance's logs/errors file, the following may not address your problem.
After deploying BIRT 2.1.1's WebViewerExample on Web Server 6.1, I was able to successfully access the index page of the web application(http://server/birt-viewer). However, when I clicked on the link labeled "View Example" the server returned a 500 Error page and the following exception was logged:
java.lang.NoClassDefFoundError: org.apache.commons.logging.LogFactory
at org.apache.axis.components.logger.LogFactory.class$(LogFactory.java:45)
at org.apache.axis.components.logger.LogFactory$1.run(LogFactory.java:45)
at java.security.AccessController.doPrivileged(Native Method)
It appears that BIRT has a dependency on Apache's commons-logging classes. I downloaded commons-logging-1.1.jar from http://jakarta.apache.org/site/downloads/downloads_commons-logging.cgi and installed it in the WebViewerExample web application (i.e. under birt-runtime-2_1_1/WebViewerExample/WEB-INF/lib). After reconfiguring/restarting my web server (reconfig/restart) I was able to successfully view the example report.
If this isn't the same as what you are seeing, then please provide more details.