I was thinking that it would be fun to have awards which a player can acquire by achieving certain feats in-game. This would be like the achievements in Halo 3, for those who have played. For example, one award might be "400 creep kills in one game", or "15 or more hero kills with no deaths". Anything interesting really. I think the Awards would add interest, as well as give players another means of gauging other players' ability to play.
I support achievement ideas in general though, always liked those systems. Gives something else to be done in games, rather than the same old monotomy.
With HoN however, I'd be careful what kind of achievements you introduce, otherwise it could screw over some games when people go purely for achievements (400 creep kills for instance, you could get someone literally just farming and ignoring everything else, just for the achievement).
To conclude, YES to achievements in general, NO to achievements that detract from the standard gameplay too much.