If you've got a Java application packaged as a jar file, try running it from the command line with
<BLOCKQUOTE><font size="1"face="Geneva, Verdana, Arial">code:</font><HR><pre><font size=1 face=courier>% java -jar <jarfile></font>[/code]
If it works, you can use MRJAppBuilder to package it up nicely as a double-clickable Mac-style app. If it doesn't work, chalk it up to Java's "write once, hope it runs somewhere" cross platform capabilities and/or Microsoft's Java "extensions" -- it probably won't work on other Java platforms, either. In this case you're pretty much stuck unless you're a Java programmer and have access to the app's source.
If it's applets, not applications, that you're talking about, ignore the previous paragraph. Applets are a lot closer to cross-platform than apps are; to run one in OS X, just point Applet Runner to the html file containing the applet. In this case, if it doesn't work, it's most likely OS X's fault.