What are all of the Runescape chat badges and what do they mean?

Solution 1:

The one in question you point out denotes a player that is an Ironman. Check out this link on the wiki. There are 7 badges currently in the game including this one.

• There are 3 crown's, gold, silver, and purple which represent Jagex Mods, Player Mods, and Community Partners (AKA Local Mods) respectively .
• The blue star shows a player who has purchased premium membership (see here). Note that player mods who have purchased this package will show a silver star.
• A red skull which shows a Hardcore Ironman.

Also there is a hidden eighth badge for Forum Mods that is a green crown. This one does not show in game though and only shows on the forums.