Blob
It's not every day you come across a book about a young woman finding a blob on the sidewalk outside a bar one night, only to wake up and realize it's real. You brought it home, and it seems to be sentient. Now what do you do!?
The premise is wild, and what grabs you by the lapels (aside from what was mentioned above) is the yearning of a young girl to belong and her willingness to believe in that possibility, no matter how outlandish or misguided the circumstances.
This book is unique, fresh, and has one of the BEST endings of any book I've ever read.