This week's book giveaway is in the OCPJP forum. We're giving away four copies of OCA/OCP Java SE 7 Programmer I & II Study Guide and have Kathy Sierra & Bert Bates on-line! See this thread for details.
For free UML, try AguUML (http://www.tigris.org). There's also a community Edition of the Poseidon UML tool (http://www.gentleware.de), which is based on the ArgoUML source, but is more polished in many ways (though also crippled in a few). If you actually felt like buying a UML tool, theirs is much more reasonably-priced than most.
For the strict DBMS/ORM type of design, check out DBDesigner. It's not a UML tool, but it allows you to graphically layout your schema. You can then use MiddleGen to build the persistency info for frameworks such as Hibernate.
Customer surveys are for companies who didn't pay proper attention to begin with.