Tony and Savvy have you on the right track to remove smaller programs which don't have obvious options to change, or which might be dangerous to remove, but I thought if you were just having a problem with an office suite, this might be the fast track to fix the problem.
If you have an office suite like Microsoft Office or Lotus SmartSuite installed, they put about 342 icons in the tray. Seems they may irritate you as much as they do me.

You can turn these particular icons off in the individual program settings.
Many programs in the tray will allow you to do this by RIGHT CLICKING on the icon in the tray, and selecting Startup Options, Preferences, or something similar. Critical Windows files will not give you this option.
If right clicking doesn't present an option, start the program you want rid of in the tray and find the Preferences or Options section, and set it not to load on startup.
Keep in mind that some automatic features won't work if you do this, and it might make some programs take longer to load. Direct CD from Easy CD Creator, for example, won't let you read CD RWs automatically if you don't let it run at startup.
On the other hand, the fewer things that start, the more RAM you will have available and the less likely you will be to have conflicts.
Never disable your virus scanner from running at startup unless you have a VERY good reason to (and don't leave it disabled for long if you do).
Hope this helps!