Search for "Java Eclipse profiler" and one of the first things you'll find is The Eclipse Test & Performance Tools Platform. I installed it, but when I went to use it, it told me my platform wasn't supported. I'm not sure what that meant - 64 bit? OS X? Java 1.6? Eclipse 3.4? I didn't pursue it, life's too short.
I looked at a few more tools but nothing stood out. There's the YourKit profiler but it's a commercial product. (Although maybe free for open source projects?) Eventually I found an article on using the built-in hprof. That sounded simple enough.
To use hprof you add something like -agentlib:hprof=cpu=samples to your Java command line. In Eclipse you can do this from Eclipse > Preferences > Java > Installed JREs > Edit. It's crude to edit the preferences to turn this on and off, but ok for limited use. (There may be a better way to do this, I'm still far from an Eclipse expert.)
This will produce a java.hprof.txt file with the results. It's fairly self explanatory.
There are more options for hprof (you can get a list with -agentlib:hprof=help)