I was introduced to Please Save My Earth by the anime- which isn't even close to being as good as the manga is. And I loved it. The manga is probably the best Shoujo manga I've ever read- the plot keeps readers guessing, the characters are all interesting, and all have very intricated and deep pasts(In the past lives, anyway- the present day characters are interesting too, though.)
The only flaw with this series is that the artwork's a bit dated- but honestly, it doesn't really matter. The series is just THAT good to get past it's artwork. I highly recommend this series, and if you love shoujo, buy this series now.