People who are exceptionally intelligent in one or more areas can be particularly difficult to choose gifts for, either because their interests are so esoteric (e.g., physics) or so focused that you are inclined to expand their horizons (e.g., no more puzzles, no more comics!). Here are some unique ideas that have the potential to be the "best gift ever." They each have the added benefit of stretching the person in a different direction (e.g., get your bookworm interacting and moving his/her body) as well as not taking up space, costing much to send, or otherwise having an ecological footprint:
For one who loves SCIENCE try MUSIC
- They Might Be Giants, Here Comes Science (favorite: "Meet the Elements")
- Jeff and Paige, Get Outdoors (favorite: "Bats (oh Baby)")
- Jeff Kagan, Songs from the Trail and (favorite: "Prairie Grasses Wave")
- Teacher and the Rockbots, Science (favorite: "Electricity")
For one who loves READING FANTASY/COMICS try LESSONS
Did you know that fencing is a sport available to kids as young as 6? Our son (age 7) is obsessed with sword fighting and took to this like bees to honey. Its an athletic, Olympic sport, and our experience is that it is populated with highly intelligent and kind men and women. Or, is your young one a budding superhero? Try Parkour, a sport I think of as urban gymnastics and very popular among youtube videos. Although it may be associated with jumping off buildings, many cities now have Parkour gyms in which kids learn how to safely vault over boxes, flip into foam pits, and scale walls. Often the same gyms ofter Aerial dance (think Cirque du Solei) lessons as well, including gymnastics in hoops and with large ribbons suspended from the ceiling.
For one who loves HISTORY try A MEMBERSHIP
Exceptionally bright children often enjoy being with adults and can hold their own among them, especially if they share the same interests. Is your child fascinated by American history? See what societies are available in your area. What about reenactment groups? Or, for other types of history (does she love dinosaurs?), is there a museum for which you can get her/him a membership under their own name? Our city has both a state history museum and smaller museums that offer special programs and publications for members. For lovers of the Renaissance, most major cities have festivals in the summer; find out if your child can get involved with the one if you are ready for that kind of commitment. Even the experience of auditioning for a bit part may be a thrill and usually held in the early spring. 
For one who loves PUZZLES try AN EXPERIENCE
Lovers of puzzles usually find their outlet in fine-motor experiences, whether on paper or with 3-D challenges, but there are many opportunities to satisfy the same mental need in other ways. Consider a year of "large puzzles": A snow maze in winter, mystery theater tickets in spring, a hedge maze in summer, and a corn maze in fall. A special trip as a family to a place that would thrill your child is a great way to help this type of child become more interactive with their interests. Hawaii has the self-proclaimed largest hedge maze in the world, the "Pineapple Maze," and Golden, Colorado has the "Miner's Maze," just to name a couple. The latter has a ropes course that requires significant problem-solving, as many do. Both rock climbing and caving (spelunking) similarly are types of puzzles that involve the whole body; look for child-appropriate programs or venues near where you live.
Any of the suggestions above (MUSIC, LESSONS, A MEMBERSHIP, AN EXPERIENCE) of course may be good for children and adults with various interests. Just remember that the best gifts acknowledge something about the receiver; a great way of communicating, "I see you and appreciate who you are". Happy holidays!