Some are wrapped and some aren't.
At our house, Santa likes to create an artful display of the presents. Each child gets one "WOW" gift - usually the biggest or most desired thing on their list, and then a few smaller ones. The WOW gift is unwrapped and usually set up ready to play. The other gifts are wrapped or not, depending on how asthetically pleasing it looks.
This has the added bonus of giving the children something to do when they first wake up (besides waking up mom at the crack of dawn).
Some examples: one year my son got a train set, and the tracks were all set up around the stack of his other gifts. Another year, he got a basketball hoop, which had a bow on it, and the basket held more gifts. Last year he got a huge wooden Swiss Family Robinson treehouse thing, and that was all set up - believe me it looked way more exciting all put together than if it was just a wrapped square.
When my oldest daughter was small, she got a play kitchen, with gifts hidden in the stove and fridge. Another year, it was a Barbie cruise ship, set up and ready to play with.
Last year my youngest got a high chair for her doll, with her favorite doll sitting in the chair, holding her stocking.
Of course when they got big things like bikes or skateboards, those just had a big bow stuck on them.