Another possibility for shoujo poor-girl-rich-boy series also hosted here is Platinum Garden, which isn't finished and has its flaws, but you might find it of interest; the art's a little more modern than Hana Yori Dango. In this case, girl is put in an arranged marriage with a rich teenager to pay off her grandfather's debt, only to slowly find that there's a lot more going on than she things.
If you want a classic shoujo poor girl simply LIVING WITH rich boys, without her life being taken over by them, there's Fruits Basket, which is here, complete, and the second-best-selling manga in America for a reason (yes, it outsells Beach). Orphaned and homeless Tohru Honda moves into the house of two boys, Yuki and Kyo Sohma, in her class as their housekeeper for room-and-board, and discovers that thirteen members of the Sohma family are curse by the spirits of the Chinese zodiac, and turn into their animal when hugged by someone of the opposite gender. Complications ensue, and much comedy, and drama -- especially once Tohru decides to break the family curse.
Haha, yes, i'm quite familiar with the Fruits Basket, seeing as the anime was one of the first ones that i saw on my very first computer. I read up on the manga around a year ago and i was not disappointed.
Platinum Garden sounds as though it might be of interest to me, but right now i want something to really sink my teeth into, and a series with the sign "Complete" after it holds my interest better i dare say, so therefore i will read Hana Yori Dango. I might check into Platinum later on.
Can't say I blame you for preferring completed series -- they're generally more satisfying for chewing through.
Another possibility is Hot Gimmick -- which is complete but not so marked in the list above. (Possibly there's some chapters missing?) Similar concept, except the connection is through corporate housing instead of school. Be warned, it's sometimes called a "manga of feminist shame" for being, well, compulsively readable (with really pretty art) with an antifeminist message.
BTW, I heartily endorse Dizzy's recommendations for Adachi's manga. Most of them are shounen, not shoujo, and have an older art style (he got started in the 1970s), but the stories are top-notch.