This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
I have been running Windows 7 since the beta came out, both 32-bit and 64-bit. Eclipse and Tomcat run just fine. Make sure you get latest JDK, and be careful of 32-bit/64-bit issues. For example, if you run a 32-bit version of Eclipse (all Windows versions before 3.6 are 32-bit only) then you will have to use a 32-bit JVM. For Tomcat that doesn't matter unless you use the Apache Portable Runtime (APR), then you will need to ensure that the bitness of the APR DLLs and JVM match. For most other Java apps, they will run just fine on either a 32-bit or 64-bit JVM, no recompilation necessary.