It's because you are selecting for your links to open in a new window/tab by having
target="_blank" in your links:
[...] of the <a href="http://www.mycasserole.net/2006/05/25/rectangle-bear/" target="_blank">rectangle bear</a>. If he [...]
I take it you are using the WYSIWYG editor? When I tried it last (a couple of versions ago), it'd ask where you wanted the link to open up I believe. Is that not there anymore?
And unless you're really attached to the WYSIWYG editor, I'd say turn it off (uncheck the box at the bottom of the "Users" screen). You'll still have quicktags there to help you out with making links and such, but you'll get to see exactly what code is going into your post instead of relying on the WYSIWYG editor.