Ok, I'm going to post my thoughts, and then go back and read everyone's posts.
Twilight- I got that right off the bat. The Bible verse in the beginning; forbidden fruit- obvious.
New Moon- I heard that Steph said she had nothing to do with the cover, but she never offered what she thought it meant (that I can recall). I think the flower represents Bella's love, or heart; her relationship with Jacob is growing, and the falling petal is her broken heart for Edward. No matter how hard she tried to move on, a part of her would always grieve for Edward; he was her first love, her only true love, and nothing can ever replace that.
Eclipse- I understood it more after I read the book... The ribbon is Bella's life; the broken strands represent the things she'd leave behind when she became a vampire; the 2 threads still connecting the 2 ends of the ribbon are for her family and Jacob, because those are the most important things in her life that she is struggling to reconcile giving up.
Breaking Dawn- I had no clue as to what it meant. I haven't read "Merchant of Venice" or "A Mid-Summer Night's Dream," so I didn't draw the comparisons. I thought that Nessie was the red pawn, and Bella was the Queen, but the more I read, that didn't seem to fit. After hearing SM explain it, yeah, it makes sense- Bella as a newborn, Bella as a strong vampire!