I would assume that to be "famous" from the internet, one could have heard of--or seen these people--outside of the internet. I think all of these people apply.
Brandon Hardesty has launched a beginning movie career from his Youtube days (artietsmitw), after Geico used one of his videos for a commercial. I think the 3rd movie he's been in comes out this year.
The "=3" guy on Youtube is also selling shirts in stores, which means that culture at least acknowledges him.
As noted, Doug Walker--The Nostalgia Critic--from thatguywiththeglasses/chanel Awesome (and a few of his crew: Spoony, Angry Joe, Linkara) are getting recognized and cos-played at events. Their site is popular enough to have raised around 90K in the past two Christmas seasons for the Ronald McDonald House. Back to Spoony--Noah Antweiler--he won last years Mashable/Webby (not sure which), which speaks magnitudes for being seen, though the internet doesn't work like a lot of otehr places when it comes to voting, polls, and popularity.
The Roosterteeth crew has also moved from the internet into a larger conciousness.
Also, James Rolffe (as mentioned, the Angry Video Game Nerd) has been asked to provide commentary for the Friday the 13th and Nightmare on Elm Street movies, which are outside the realm of the internet.
Liam Sullivan (from the "Kelly" vidoes) is also now semi-famous, having appeared on several shows/tie-ins.
Nathan Barnatt (Talking Classics on Screwattack) is also an often used actor for commercials.
Others have been mentioned, but this is my list. Whiel they're not all "famous" in the traditional sense, they are all now rather "successful," and have bridged the gap from internet to reality, or internet to other medias.
As for people on this site, Bob Chipman is a name recognized by some who I talk to, known here as Movie Bob, and as the Game Overthinker on Screwattack, as well as his own site.
Yahtzee is also well known for his scathing reviews.
I also recognized Lisa Foiles from Angry Joe, and recognition is a sort of fame.
These are, at least by my opinion, people who have either become known on the internet, or known outside of it for more than just being part of a "viral video."
Famous or not, they are doing well.