My go-to present is more a category -- block puzzles, where you have (usually) 16 blocks, and you can make six pictures from them. Small kids can stack them, and as they get older they can also put them together to make the picture. So it's good from about age 2-7, or for families with kids of different ages.

Along the same line I had some floor puzzles made from thick foam that made complex pictures, but all the pieces could snap together. So the 2-4 year old could just randomly assemble them (until he went to bed and OCD mom did it "right" before putting it away) and the 0-1 year old little brother could have a mat to lie on. My google-fu is failing me, but they weren't hard to find fifteen years ago...