When thinking of astronomy, often the first thing that comes to mind is a telescope. Telescopes are expensive, so this would be for someone very special. But a word of warning on buying a telescope is probably: Don't. An exception would be if it were for someone who wanted one and already knew the sky well enough to use it. It would still be a good idea to consult with this person first and have a look at "Choosing and Using a Telescope". (There is a link below this article.)
Telescopes are more often put away and ignored than they are used - as well as being expensive. Binoculars might make a better present. They are easier to transport and store than a telescope and you can use them for other hobbies. (Click on the link below the article to find out more about observing with binoculars.)
Now onto some more useful general options.
A DVD could be welcome, especially for a series the person missed or might like to see again. A quick look at Amazon shows astronomy DVDs from National Geographic, the History Channel and Nova, among others. There are also films such as David Sington's superb In the Shadow of the Moon, which I have reviewed on this site. (Link below this article.) You probably have local stores that sell them too.
There are lots of great astronomy books around, though alas, a number of books are all gloss and no substance. But for a comprehensive look at the universe, I highly recommend Universe, written by a team of experienced astronomers. There was a brand new edition out in October 2012 and it's gorgeous. It has the story and the pictures and would be a great present, if you can bear to give it away. (Dorling Kindersley, ISBN: 978-1409376507)
If the person you're buying for doesn't subscribe to an astronomy magazine, a subscription could be a thoughtful gift. Sky & Telescope and Astronomy are USA magazines and Astronomy Now and Sky at Night are based in the UK. In addition, their online stores don't just offer subscriptions to the magazines, but a selection of books, maps, posters and other items.
Astronomy Now presents European Astrofest in London one weekend in February of each year. Tickets to this event would be a wonderful present for someone living in - or visiting - Europe. It is two days of exhibitions and a fantastic line-up of speakers.
For many years now, I have bought annually the Year in Space desk calendar, and have also given it as a present. It has pictures, information, anniversaries and plenty of space for your appointments and notes. If you subscribe (free!) to their e-newsletter, you can claim a discount too. In 2012 they also started offering a beautiful wall calendar.
Do you have a nearby planetarium or science museum? A visit or gift voucher might make an unusual gift. They also tend to have gift shops, some of them quite extensive and interesting, as well as online sales.
Although I have never bought anything from Edmund Scientifics, I've browsed through their online catalog. It has an intriguing selection of science-based items, including astronomy ones.
SpaceToys.com, located in Connecticut, USA, was started by a space enthusiast. Their catalog has a great selection of space-related objects. It isn't just a toy shop, however. They sell genuine space memorabilia, along with such things as T-shirts, models, posters and astronaut food. They say astronaut ice cream is one of their best sellers, but though I've never tried it, I suspect I'd prefer Ben & Jerry's!
But for a present that won't break the bank, there are two well-known companies that specialize in putting slogans and pictures on just about anything, Zazzle and Cafe Press. I looked through dozens of pages on each site, but there are hundreds of pages of items. You can get get posters, T-shirts, mugs, hoodies, stickers, bags, notebooks, hats, water bottles, blankets, puzzles and more. If you don't see the design you want, you can design your own. These companies operate internationally, so you can save on delivery charges by choosing the nearest one to you.
If you have anything to recommend, please let me know.
(1) European Astrofest
(2) My report on Astrofest 2014.
(3) The Year in Space