One of the things that inspired me to re-write a Jane Austen novel was the webseries The Lizzie Bennet Diaries. Since that series ended I've found several other webseries adaptations of classic stories - and I'm going to share my faves.
The format is usually easy-to-digest short episodes of 3-5 min each. Perfect for procrastination breaks! Because the distribution platform is (usually) youtube, it makes it possible for smaller, independent productions to find an audience (that isn't to say it's easy, just doable compared to getting a studio to pick up your show). The other interesting aspect of web-series is the potential for transmedia elements - the idea that characters from the show can have twitter or tumblr or pinterest accounts, for example. So you can just watch the videos or you can delve deeper into the show and see twitter conversations between characters, or get a sense of the character's mood based on tumblr posts, possibly even interact with characters.
Some of my faves:
Lizzie Bennet Diaries - a modernization of Jane Austen's Pride and Prejudice done in the form of a vlog (video blog). Very well done. With amazing chemistry between Lizzie and Darcy. It's interesting to note how the use of a vlog as a medium inherently changes the character - here we have Lizzie as a person who posts videos of personal conversations on the internet. The Lizzie I picture from P&P wouldn't do that, but if you can make that adjustment, you'll get on fine. I followed the character twitter accounts while I was watching this show roll out and I got really obsessive about it - those little extra bits of character development were awesome. They had a big fan following - mounted a successful crowd-funding campaign to produce DVDs, and have just released a book (Lizzie's actual diary). www.lizziebennet.com
The Autobiography of Jane Eyre - by a team in Vancouver. A modernization of the Bronte novel. This is a tough storyline to update and I think they did a good job. Some wonderful characters, creative vlogs.
The New Adventures of Peter and Wendy - I heard about this one and originally passed on it because I wasn't really interested in a Peter Pan story. Then I somehow watched episode one and fell in love with the characters and proceeded to watch the rest of season 1. It's so charming and lovely. I love it to bits. They are currently crowd funding to try to do season 2 (and 3); I've donated - I hope they make it!
A nice list of the many indie webseries adaptations can be found here (there is a Green Gables one underway, I think).