The kids are all but grown now, but for you guys just starting a tradition, here's what we did.
Every year, something BIG was under (or near) the tree.
Completely unknown to the kids & not on their list.
Not terribly expensive, but BIG and IN the house.
In no particular order:
Pool table (cheap one, but full-sized & assembled, arg!)
Ping-Pong table (twice, several years apart)
Canoe (a big ugly red Coleman; lots of smiles)
Go-Kart, 2 seater (group effort from grandparents & us)
Motorcycle (very used, but prettied up, new tires, etc.)
Bicycles (SIX of these one year)
Tents (every kid LOVED playing in their OWN tent)
Various ride-on toys, some electric, some not.
Arcade-style basketball goal (the kind that keep score)
One year, when the boys were young, with the help of friends, I moved a BIG free-standing fort into the yard in the middle of the night. (I had pre-fabbed it in the warehouse at work, after hours.)
All of these things were set up, put together and ready to use.
If it has rechargable batteries, charge them up.
If it uses batteries, put some in it (keep extras around).
Look at the way toys are packaged.
Cut ALL those tie straps & wires loose, so that the kid can get it out of the package.
This year, my youngest boy already knows he's getting a tree stand (he got home before I did & saw it on the porch, where UPS left it). I plan to install it high in a tree, thirty yards from his target. It will be set up so that he can practice with his bow, Christmas morning. But he will have to find it.
Make sure whatever you get is age-appropriate.
(A well-meaning uncle bought a train set & a wood-burning kit for my then-four-year old.) Both were sources of frustration for myself & the kid.
If the package says "twelve and up, wait until the kid is twelve. He/she will get there in the blink of an eye.
The elderly couple next door (among others) let us hide the "big" items in their garage. They got a big kick out of helping with Christmas, and would come over to watch the kids play.