How can I open Java .class files in a human-readable way?

jd-gui is the best decompiler at the moment. it can handle newer features in Java, as compared to the getting-dusty JAD.

As pointed out by @MichaelMyers, use

javap -c <name of java class file> 

to get the JVM assembly code. You may also redirect the output to a text file for better visibility.

javap -c <name of java class file> > decompiled.txt

If you don't mind reading bytecode, javap should work fine. It's part of the standard JDK installation.

Usage: javap <options> <classes>...

where options include:
   -c                        Disassemble the code
   -classpath <pathlist>     Specify where to find user class files
   -extdirs <dirs>           Override location of installed extensions
   -help                     Print this usage message
   -J<flag>                  Pass <flag> directly to the runtime system
   -l                        Print line number and local variable tables
   -public                   Show only public classes and members
   -protected                Show protected/public classes and members
   -package                  Show package/protected/public classes
                             and members (default)
   -private                  Show all classes and members
   -s                        Print internal type signatures
   -bootclasspath <pathlist> Override location of class files loaded
                             by the bootstrap class loader
   -verbose                  Print stack size, number of locals and args for methods
                             If verifying, print reasons for failure