Some Austen novels have lent themselves well to updates. The movie Clueless is an outstanding example; it's basically Emma told with a teenage, well-to-do Valley girl named Cher Horowitz in place of the well-off, headstrong Emma Woodhouse. Clueless had to make some changes in the story line, the biggest one being that Cher was in high school and the story doesn't end with her getting married.
We recently got cable TV (actually FiOS), and I watched the movie Bride and Prejudice, a Bollywoodish retelling of the P&P story with a rich American man falling for a young Indian woman with three sisters. I was surprised at how well the story fit, and then I realized it was because traditional English culture is a lot like 19th century British culture— arranged marriages, no public kissing, women were expected to get married, and filial respect is a big deal.
On the other hand, it's always interesting to see how updates change plot points to fit the culture. Emma falls for a neighbor whose brother is married to her sister, making them kinda, sorta sibling-like, but not really. In Clueless, the modern version of that is that Cher falls for a guy whose mother used to be married to her father.
In the original P&P, the wicked Mr. Wickham had tried to persuade Mr. Darcy's 15-year-old sister to elope with him so he could get his hands on her money. In Bride and Prejudice, Mr. Wickham is even more wicked— he gets Darcy's teenage sister knocked up and then tries to get her to elope. They never mention whether she had the baby or not. Back in Austen's England, a premarital pregnancy would have made Miss Darcy no longer respectable, so the plot was foiled in time.
In any event, I think Jane Austen would have been pleased. If imitation is the sincerest form of flattery, we must all like her a lot!