The first that came to mind was actually another Amy Ryan role -- Beadie on season two of The Wire. It took awhile for me to get into the whole dockworkers storyline, but it was Beadie that helped me through.
If a show plans to stay on air for awhile, it needs fresh blood -- but the process of introducing new characters isn't easy (witness how reviled Maya was on Heroes). The best new additions combine great actors with well-written characters.
Here are seven other (fairly recent) new characters that succeeded.
A long time ago, on an Internet far, far, away, the creators of the NBC series Heroes decided that a weekly webcomic series would coincide perfectly with the show they were producing. I mean, Heroes is about superheroes. So, during the first season of the show, a different artist penned a short webcomic (about five pages long) that focused on the background of one of the characters, or introduced a new character not seen on the television show. Eventually, all 34 chapters of this webcomic were collected and sold as a graphic novel. All was good in the galaxy.