I started "reading" books to my daughter when she was about 5 months old. We started with soft cloth books with few words and interactive pieces, like a joey that can be put into/ taken out of the momma kangaroo's pouch. She loved these, and after a month or two of just those we started with a few classic board books. She was very, very engaged while I read them to her. When I would get to the end of the words on each page, she would turn the page herself. She would also point to the different characters/ animals/ objects as I mentioned them. By about 8 months she would crawl over to the bookshelf and grab her favorites, which she could recognize from the spines. At about a year she started pointing to letters and asking what they were, and by about 15 months she could tell you almost any letter of the alphabet if you pointed to it. She started reading early and is now (at 9) a very avid and above grade level reader. Her sister was never quite as into the books as she was, but definitely enjoyed being read to, especially non-fiction (a preference that started as an older infant and continues now at 8).
Aside from all the perceived benefits of reading to infants, it was definitely one of our favorite activities to do together, and there are many, many great books for young kids.
Our favorites included: Dr. Seuss books, Jamberry, Take Me to the Zoo, Goodnight Moon, and Eric Carle books (I actually didn't really like Eric Carle personally, but my kids loved them, especially #1).
Also, I made it a point to show my daughters not to chew/ rip books when we were only reading the cloth books, and we never had a problem with destructiveness towards books later. I honestly had more books ruined by my pets than the kids! Once they graduated to "real" books (non-board) we had plenty of accidental tears, but that's just part of life. Plus the binding on a lot of kid books (especially paperback) just doesn't stand up to normal wear and tear.