I'm a big fan of Wysija. The plugin has allowed me to create a newsletter that has the look and feel of my blog, and according to my SMTP provider essentially all of my emails get where they're going. I like the double-opt-in feature, too. Bonus: the support has been great. I came across what I think was a problem in the latest update that was keeping my newsletter from displaying properly, and within a few hours the developers had sent me a file that I uploaded to my server and that solved the problem.
My only unhappiness: I make a lot of use of the Simple Footnotes plugin, which lets me use a shortcode to create footnotes that, when viewed on the web, properly formats footnotes so they appear at the bottom of posts. Unfortunately, Wysija doesn't recognize shortcodes, as far as I can tell, and so when I have a post with footnotes, it doesn't translate well to the newsletter. I hope the developers will consider allowing users to enable shortcodes!