It depends. Many toys now come with batteries already which is a plus. Those darn twist ties are a real pain. I usually just wedge a good pair of scissors in there and cut them as gifts are opened.
Now for the big items (ie kitchen for DD, tool workbench for DS) yes we take them out, and set them up. Depending on the size I either leave them out in the open, or put a huge gift bag or tree bag over the top of them. Smaller items-if it already has batteries, I keep boxed up unless it is something that could easily be wrapped alone. The twist ties keep the items from moving around too so I usually leave them intact. I like to keep things in the boxes (especially the smaller items) until all the wrapping paper is picked up and thrown out. I think we have lost toys in wrapping paper over the years.
alison