You absolutely should!You won't be dissapointed.
To be honest, I knew nothing of the books until I was taken to see the movie.
I then went home and picked up book 2 from where the movie left off (skipping book 1 all together) and it took me 3 days to read the last 3 books! Stephenie Meyer did a great job with these books. Sucked me right in, and I don't even bat an eye at books with topics like this! I'm a non-fiction kinds girl traditionally.
It helps that Robert Pattinson played Edward Cullen. I've been familiar with him since he began in Indie films.