Anything by Richard Scarry. Things that Go was my kids favorite.

All good stuff. I would just add The Very Hungry Caterpillar (they love to stick their fingers in the holes) and any of Richard Scarry's Busy Town books.

Great suggestions. I'd add Goodnight Goodnight Construction Site, and Owl Babies (this one helps with mom separation)

Are you my mother? is another great one.

I second the Brown Bear Brown Bear book with the sliding windows. My son loved it when he was tiny...and we still read it occasionally now that he's four!

I am a Bunny by Richard Scarry, another one that had staying power for some reason.

Great recs above. I'd add:

Chicka Chicka Boom Boom
Don't let the Pigeon Drive the bus (and others in that series)
The Cow, Pig and Dog series
And Glow in the Dark books. Those are a huge hit and great for bedtime and encouraging turning out the lights. If it's for a boy there are a few Thomas the Train ones, and there's at least 2 Dr. Seuss themed ones.

At that age, my twins loved Goodnight Moon, Goodnight Gorilla, the Sandra Boynton books, Russell the Sheep, Sheep in a Jeep, Berenstain Bears beginner books (Inside, Outside, Upside Down, and Old Hat, New Hat, etc), Five Little Monkeys (we would sing the song as we read the book).

My son's favorite books at 1 year old:
Karen Katz Lift the Flap books
touch and feel animal books
slide and find books like Brown Bear, Brown Bear, What do you see?
Pat the Bunny

Basically any book that is interactive like that

He also loves all Dr. Seuss. We have the miniature, abridged board book version and the larger, hardcover version of many of the classic Dr. Seuss books. We have been reading the board book versions for a long time and at 18 months now, he just recently started developing the attention span to sit and listen to the longer versions too so I think one version or the other of these are good for all ages.

Sandra Boynton Books (Going to Bed Book, But Not The Hippopotamus, etc)
Eric Carle (The Very Hungry Caterpillar, Brown Bear Brown Bear)
Little Blue Truck
I am a Bunny
Night Cars
Dr. Seuss books
Go, Dog, Go
Pete the Cat (I Love my White Shoes)
If you Give a Mouse a Cookie series
Pout Pout Fish
Mighty Dads

Pout pout fish
Giraffes can't dance

The Little People lift-the-flap are a constant favorite around here.

Big Red Barn was my absolute favorite kids book for when my DD was 0-3.

At one, my kids all loved touch-and-feel books. I like the "That's not my ..." Series, but any will do.

Other favorites : Dear Zoo, Goodnight Gorilla, Jamberry, Click Clack Moo, anything by Sandra Boynton, Little Blue Truck, everything Eric Carle, Dr Seuss has some good ones for younger ones, etc.

Moo baa la la la
Hippos go berserk and all the other Sandra Boynton books to start.

I want to get some books for a friend's child and am looking for books starting 9 months all the way up to 2 years. Although I have two kids of my own, my memory is completely failing me except for a couple of books.
I am asking for a wide age range hoping to get the baby a good collection that will last a little long. This is their first baby so they don't have many books yet. Thank you!!