The only way I know of is to go into each forum, in the top right hand corner it says 'Mark Topics as Read' or some such, if you click that it will clear it. Not sure if there's a way to do every forum at once though.
Battle.Net ID: Penguins#1368
D3: Wizard/Crusader/everything, Clan <SC>
World of Warcraft
Kilrogg - Alliance