You definitely DO NOT want to use the attribute on links to your own pages. Do that, and you'll deprive your own pages from the chance of influencing how your other pages rank.
Having said this, I've no doubt some people will try playing with the new tag as a means to "hoard" PageRank that's passed on to only a few pages in your site. For example, your home page might link to 25 of your internal pages. Using the new attribute, you could exclude all but five of these pages. Do that, and you might possibly cause Google to give those five pages more credit.
Maybe. Perhaps. And perhaps the search engines may make other changes down the line. Rather than get tricky with this tag, I'd recommend using it as intended for now -- as a means to flag that there are certain links on your web site that you didn't place there.