One particular guy, iconscraper, is automated--he's set up a program to scan the feed LJ sends out which has people's icons on it. This process means that he hotlinks to all the icons he "scrapes" up. He think's there is nothing wrong with what he's doing and is pissed off that people are pissed off that he's stealing their icons and their bandwith. What a charmer, eh?
Anyhow, there is a way to keep people like him from linking to your icons/images and stealing both them and your bandwidth.
To remove your own journal from these feeds go to The Admin Console and input type set latest_optout yes and click on the execute button. Make sure that you are logged into LJ when you do this.
If you run a community, type set for communityname latest_optout yes, replacing 'communityname' with the plain text name of your community (no lj code).
ETA: As uniquewonders has just pointed out in comments, you can also set your syndication level via the Admin Console:
set synlevel option
set for communityname synlevel option
The options are:
* full - includes full entry text
* summary - includes excerpt of entry text
* title - includes subject lines only
set synlevel summary
set for bloodclaim synlevel title
You can see the links to your feeds and therefore what their content is in this FAQ.
ETA2: Also courtesy of uniquewonders, here is a link to a comprehensive list of privacy settings you can tweak to suit yourselves.