I was hoping to use My Side of the Mountain because I really think it would interest them.
I'm pretty sure the reading level for My Side of the Mountain is 5th grade. Unless your students are very advanced readers, it wouldn't be the right level for guided reading in third grade.
These are all end of 3rd grade reading level (DRA 38-40)
Mouse and the Motorcycle
Ralph S. Mouse
Tales of a Fourth Grade Nothing
The Trumpet of the Swan
How to Eat Fried Worms
These are mid-third grade level: (DRA 34)
Ramona series chapter books by Beverly Cleary
Beginning Third Grade level: (DRA 28)
The One in the Middle is the Green Kangaroo
These are all books I've used for literature circles in third grade, depending on the reading level of the students. Even when I had advanced readers I tried to keep the subject matter appropriate for 8-9 year olds. Many do not have the schema to understand the subplots and deeper comprehension in advanced chapter books.
I also agree with a PP that Magic Tree House series is a great series for third graders, and the books range all the way from 2nd grade to end of 3rd grade level so there is something for everyone.
I have always found that classic literature, like many of the books listed above, appeal to the children of the new generation as much as they appealed to us when we were kids. They are good stories with good vocabulary, and are stories that are unlike the stories in the new cartoons, so they are a novelty. I wouldn't worry very much about the stories being "updated" as I would about making sure they are reading good literature.