Warning: I usually try and be very "holiday-generic" during this time of year, so forgive this post. Unfortunately, in terms of books, we go totally Christmas overload...I'd love to hear other non-Christmas suggestions in the comments!
Every year growing up, my mom bought a Christmas book. She would write a few quick notes about the year (e.g., "moved to elm street, got a dog") on the inside cover. Thirty-plus years later, she has a wonderful collection of Christmas books and we have fun reminders of our family milestones. I plan on doing the same for my kids...of course, I'm just starting so I have to buy a stack of book this year and back date them! Here are some suggestions, beyond the The Polar Express.
The Night Before Christmas: It's a good place to start the collection. Jan Brett has wonderful, detail rich illustrations. Actually, any of her books are perfect for a holiday/winter collection. I also like The Mitten board book. They often have these at Costco.
The Sweet Smell of Christmas: This is in my mother's collection. We loved it growing up. Seriously, I didn't even know they made scratch and sniff anymore - but they do!
Snowmen at Christmas: Fun story about snowmen coming alive at night. It's like Frosty, but the illustrations make it seem more magical. A simple story good for little ones too.
I'll Be Home for Christmas (Toot and Puddle): Darling story about beloved Toot and Puddle. And you'll see some familiar Boston scenes. This story is a bit more complicated (at least you'll need to be a bit older to pick up on the magical "helper"), so probably better for 3-4 years plus. Although you can always look at the illustrations!
Where is Baby's Christmas Present?: Karen Katz always creates darling board books before for the under 2 set. Simple, graphic illustrations with flaps to keep babies busy.
Your favorite characters (e.g., Olivia, Arthur, Berenstain Bears) all have Christmas books too. What are your favorites?