Russ Olsen has posted 10 Unix things every Java developer should know on http://www.javalobby.org/articles/10things-unix/, +1 to that. I am going to post 5 more (didn't feel like adding unnecessary ones to make the magic number 10). Here are my picks in no particular order:

1. Know file permissions: Unix assigns read, write and execute permissions to owner, group and others. If you are going to be running scripts, installing software or simply copying files from another resource, you will need to understand and most likely change file permissions. Good luck learning chmod 755, chmod a+x, chown -R and more
2. Know how to use ssh (secure shell) and the tools that use ssh to allow login to remote machines. There are times when Unix servers don't allow telnet and/or ftp but allow ssh. Sometimes, you also need to download some files and use scp (secure copy or copy over ssh) to move it to the server. Checkout Putty and Cygwin
3. Know basic file operations: You should at least know how to create, delete, copy, move and rename files. It's pretty much a crime to change configuration files without saving a backup first. Learn basic vi editor commands. I like this page for vi help: http://cac.uvi.edu/miscfaq/vi-cheat.html
4. Know various archive utilities: Most of the stuff you download for Unix will be in tar and/or gz format. It is a good idea to learn to work with those utilities. Just knowing how to extract an archive or create one isn't enough. For example, how would you extract an archive in a different directory?
5. Learn to use the log files: If I were listing the items in any order, this would have been number one! Learn to tail a log file so that you can keep an eye on it while it's changing, learn to list log files by timestamp so that you are sure to look at the last one, learn which log file is updated when. For example, on my WebSphere Portal project, I have to look at trace.log, SystemOut.log, SystemErr.log and wps_$timestamp.log files in different situations. If the server doesn't start properly, I have to look at SystemOut.log and startServer.log. Occasionally, you will have to send log files to support group to get their help fix a problem. You may also need to update properties files that control how log files are updated and what is logged
6. Alright, here is a bonus one: Learn to type fast (this one needs no explanation)