Somehow I missed doing a book round-up at three, so here's one at three and a half (the last one was at two). This is by no means complete, it's just a few of the more notable works. As you'll see, most of these were recommendations from friends, so I feel I should pass them on further.
Arnold Lobel's Frog and Toad books (hat tip Frieda/Nadia)
These have been a staple of bed-time reading for the last four months. There are four books, each with five stories of around twelve pages.
They are "early reader" books, with simple sentences and restricted vocabulary, but they are remarkably sophisticated given those constraints. See the Atlantic essay "Frog and Toad and the Self" for an explanation of how this works. The "Collection" only contains three of the books, which we augmented by buying the missing one, so I would recommend getting the hardcover Storybook Treasury which contains all four books (Amazon UK, Wordery).
In the same Early Readers series, we also enjoy Russell Hoban's Frances books (hat tip Immi/Kat).
Shinsuke Yoshitake's It Might be an Apple
This is surreal in an entertaining and appealing way, and visually quite entrancing as well (Amazon UK, Wordery). This was a chance discovery in the Old Hall bookshop in Brackley. There's a second book (with the same protagonist, in a similar vein) Can I Build Another Me? but that wasn't quite so much of a hit (it might work better with slightly older children).
Alice's Adventures in Wonderland and Winnie-the-Pooh
These will need no introduction. Helen has just reached the point where she will comfortably sit through a chapter of Alice or a Winnie-the-Pooh story. Though she sometimes wants more pictures, mostly any complaints are about slightly scary events. I've just replaced a beaten up old paperback Alice with a nicer one (Amazon UK, Wordery) and we have a boxed four-book Winnie-the-Pooh set (Amazon UK, Wordery).
Allison Uttley's Little Grey Rabbit stories (hat tip Sally Bayly)
These are fairly obvious Beatrix Potter look-alikes (from the 1930s, so the language is a bit more modern), but nicely done (Amazon UK, Wordery). In a more modern vein yet, I have picked up a Complete Brambly Hedge on sale, but we haven't tried that yet.
Jane Hissey's Old Bear Stories
This is a series of stories about toys who live in a house by themselves. We first encountered one at nursery, then I picked up Old Bear Stories at the Broadleaf bookshop in Abergavenny (Amazon UK, Wordery).
Jenny Koralek's Mabel's Story (hat tip Katja/Kristina)
We've had this around for a while, but it's only just taken off. Grandpa's non-directive prompting and encouragement of Mabel's storytelling is a lesson in itself. Now out of print.
The Puffin Book of Fantastic First Poems (hat tip Rachel/Lucy)
This is one of the nicer poetry anthologies for younger children I've seen. It's plentifully illustrated, and the poems are a good combination of traditional and more recent (though editor June Crebbin perhaps includes a few too many of her own poems).
Ian Beck's Peter and the Wolf
There are many versions of this, but Beck's illustrations are lovely. The text follows Prokofiev fairly closely, and we follow along with Bramwell Tovey's combined narration/direction of the Vancouver Symphony Orchestra.
There's been an unexpected revival of interest in old board books such as Owl Babies, Who Am I? Snowy Animals, The Very Hungry Caterpillar, and Toddle Waddle. Possibly because several months ago I (once, in passing) suggested we could get rid of the first two of these, but perhaps also because she also knows them almost off by heart and thus can "read" them herself.
Helen is very keen on the one Sarah and Duck book we have, but I'm not so taken by it - it doesn't really capture the spirit of the television program, and doesn't stand up to multiple rereadings.
I really like Aaron Becker's wordless Journey (Amazon UK, Wordery), but after a few "readings" Helen decided it was too scary and though she picked the sequel Quest to buy in a bookshop, never took to that either.
And interest in the Paddington and Madeline stories has disappeared completely, despite my occasional suggestions.
We've read the first book of Mango and Bambang stories (about a girl and her tapir), but they're a little bit long for Helen and bits of them are a bit too scary.