Here’s my list.
Rendevous With Rama - Arthur Clark
Downbelow Station - C J Cherryh
Beyond the Blue Event Horizon - Frederick Pohl
Startide Rising - David Brin
Ringworld - Larry Niven
Norstrilia - Cordwainer Smith
The Forever War - Joe Haldeman
Dying Inside - Robert Silverberg
Way Station - Clifford Simak
The Marching Morons - Cyril Kornbluth
Yeah, pick on me - BrainGlutton suggested the whole trilogy. I re-read the first book a while back and though I remembered it as being bloody epic I found it moved a long quite snappily, quite a lot happens after all. It is a bit pretentious* and there aren’t many laughs 
but I think it can be defended as a decent bit of SF.
*like, really, really pretentious.
I agree with Voyager. I would suggest a collection of short stories from the “Golden Age of Science Fiction” as a good introduction to the genre:
Adventures in Time and Space is the definitive collection.
I, too, agree. This anthology, now about 60 years old, but, I think, still in print, has “stories of wonder” straightforwardly told that will introduce the new SF reader to almost all of the concepts developed by later writers. It is fun to read! It was what got me hooked on SF. I would not give a beginner any of the current “Best Of The Year” anthologies that come out every year; most of them contain stories so dark, deep, convoluted, and so distantly related to traditional SF that they would drive a new reader away.
I’m not sure anyone has recommended anything written in the last 30 years; maybe the Robert Sawyer. Oh, and I guess Snow Crash is only 18 years old. Does anyone have some possibilities from more recent fiction? I can’t recommend much myself; the recent stuff I’ve read (mostly by Scottish writers, Stross and various people named Ian) don’t strike me as super accessible. Double-plus ditto Greg Egan.
I did find OLD MAN’S WAR by John Scalzi readable and pretty accessible (fair amount of sex in there if you’re worried about that for a young’un).
Going back to semi-aged stuff, if you can find it, Growing Up Weightless by John M. Ford is great, the closest thing to a Heinlein-juvenile-with-a-more-modern-sensibility that I can think of.
Lois McMaster Bujold’s Vorkosigan books are great, though I hear the first two aren’t as good (never read them myself). Still, especially for a younger reader starting at the beginning of the story is probably a good idea; I think the first set are collected in Young Miles.
The lists of books that I would recommend would depend a lot upon both the tastes of the reader, and the purpose of reading the books. I hate a lot of the books that have been recommended, for various reasons. And while I liked Dune, for instance, I certainly wouldn’t give it to someone who has never really read SF before. I would start with The Moon is a Harsh Mistress by Robert Heinlein, and then probably follow up with any of his “juveniles”, because they are, IMO, both well written and well told.
If you can find any of the old Groff Conklin anthologies, yes, get them. Some of the stories will be outdated, but they will all be good reads. I’d also get the Hugo award anthologies. I have been very pleased with most of the L. Ron Hubbard’s Writers of the Future award winners anthologies. By reading the Hugo anthologies, the reader can learn which authors s/he likes, and which s/he doesn’t, and can choose more books by those authors. Most of the authors in the Writers of the Future anthologies just have one or two short stories in their idea box, but they are still good reading. There are also some annual “Best of SF” anthologies, some of which are pretty good, some of which are not.
Really, it’s pretty hard to come up with a definitive list of just 10 great SF books. Also, it’s possible to like some of an author’s works, and dislike others. For instance, I loved David Brin’s Kiln People, Glory Season, and The Practice Effect, but I could never get into his Uplift War series, and I’ve tried several times. And I like Larry Niven alone and when he writes with others, but I can’t stand one of his frequent co-authors (Jerry Pournelle) when Pournelle is writing solo.
Once you find one author you like, try using this tool: http://literature-map.com/ . I get some dud results, but I’ve also gotten some really great recommendations.
Here’s a recent threadabout newer science fiction books that I started. It might be good for ideas.
There has been some good near-future hard SF out in that period:
Anything by Robert L. Forward. Very hard SF, Forward was a physicist. And yet, with grand, wild ideas! Dragon’s Egg is already a classic; it’s about a neutronium-based race of sentients living on the surface of a neutron star.
Ben Bova’s Grand Tour series – all set within the Solar System and within the next 100 years.
Allen Steele – lots of stuff about the daily lives of astronauts in LOE, on the Moon, etc., and in the near future. For something farther out (in time, at least) see A King of Infinite Space.
All of the above resemble Golden Age SF in being straightforward storytelling with fast-paced plots, not dark or convoluted at all (well, not much), with plenty of sensawunda, and no visible effort being made to impress the English profs. (See the TVTropes page Scifi Ghetto.) Very, very accessible to the newbie reader.
It didn’t look in print at Amazon, but the complete paperback version is readily available. But the hardcover starts at almost $50 - I’m rich!
if a person wants classic stuff and their tastes run less to hard science fiction, some of the Unknown era work by de Camp might be good. I don’t know if the Unknown anthology is still in print, but those stories are fantasy while still being logical.
There was a long series of anthologies taken from F&SF - at least 15, I think, and they are pretty good also, though out of print.
I’m out of touch with the field, but…
Ender’s Game – Orson Scott Card
(pretty mean spirited, which is part of the reason for its popularity.)
Flowers for Algernon – Daniel Keyes
(a soft-science classic. Very character driven.)
Mote in God’s Eye – Niven & Pournelle
(Most early Niven is good. Mote is a big book full of action and ideas )
Glory Road or Puppet Masters or **Tunnel in the Sky (**juvenile) – Robert Heinlein
(I don’t care for any of his Big Books. The ones listed are easy, involving stories)
Lord of Light – Roger Zelazny
(although This Immortal/Call Me Conrad might be more friendly to beginners)
**Do Androids Dream of Electric Sheep **-- Dick
(actually I barely remember the book, but Dick is Special and I think that was a good one… don’t care as much for his more famous books like UBIK or High Castle.)
The God’s Themselves – Isaac Asimov
(Fine book by a famous author.)
Rendevous with Rama – Arthur Clarke
(Fine book by a famous author.)
Slaughter House Five – Vonnegut
(if you like him, you’ll usually love him. Very easy to read with lots of tiny paragraphs.)
900 Grandmothers – R. A. Lafferty
(Tall tales and fantasy, but close enough to science fiction to qualify for this list. Lafferty --like Dick-- is unique.)
I’d like to get in recommendations for Sturgeon, Poul Anderson, John Varley, and Bradbury, but can’t think of a non-fantasy volume that would knock off one of the above.
My List:
Ender’s Game by Orson Scott Card.
-A scarily empathic and intelligent boy get sent to battle station to learn and teach tactics useful for interstellar warfare.
The Dark Beyond the Stars by Frank M Robinson.
-This is a nifty book about the search for identity on a generations long exploration of the Galaxy. It also neatly summarizes the major arguments for and against life as a widespread phenomenon versus a one-off event on Earth. Every time I found myself anticipating a plot revelation the book took a ninety degree turn.
On Basilisk Station by David Weber
The introduction to the Honor Harrington series. An ever wider sprawling space opera, but the first few books were fairly tightly focused and ripped along quite nicely. As mentioned above it was consciously based on Horatio Hornblower. This is available at the Baen Free Library in various electronic formats so you can try it for free.
The Past Through Tomorrow by Robert Heinlein
-This is a collection of Heinlein’s short stories and novellas all set in an alternative (Future History) time line. You get a flavour of his writing style and several key stories. These also provide a shared backdrop for many of his later novels (Time Enough for Love being one of my favorites).
Cordelia’s Honor by Lois McMaster Bujold
-An omnibus edition containing her novels Shards of Honor, and Barrayar which relates the story of how Miles Vorkosigan’s parents met and why Miles is the way he is. It serves a good intro to the Miles Vorkosigan saga, which itself is well worth reading.
Expendable by James Alan Gardener
-The first League of Peoples book. This introduces the series main protagonist and gves us a universe where Humans are not the apex of culture or evolution. The edict “thou shalt not kill” is thoroughly enforced, so how do you navigate and explore the universe under those rules. The entire series explores different questions about destiny, evolution, and ethics all being cloaked in various (usually murder) mysteries. Vigilant and Trapped are better books but Expendable is where it starts.
Valor’s Choice by Tanya Huff
-The first in a series of four books. Staff Sgt. Torin Kerr is a no-nonsense space marine sent on a multi-species diplomatic mission to convince a reptilian race to join the civilized side of a Galactic War. Just off a particular grueling mission she and her marines are sent off to meet new people “and not shoot at them, for a change.” Things go horribly wrong. I recommend this primarily because of the humor in the story as well as the little cultural details she gets right in writing about other species. Also you get to play spot the Canadianisms now and again.
A Princess of Mars by Edgar Rice Burroughs
-My first “Sci-Fi” series and is a nice “what if?” exploration of a Lowell-ian Mars, and is a decent tale even if Science Marches On. The full text is available via Project Gutenburg.
The Forever War by Joe Haldeman
-A book essentially about the Vietnam War. The main character is conscripted into a war that sends him on a one way trip into the future thanks to time dilation effects. While he and his comrades are away fighting, various culture shifts take place at home. A good intro to Sci-Fi as direct allegory.
Dune by Frank Herbert
-Possibly one of the best examples (or at least widely acknowledged) of world building in Sci-Fi. While it may be a slog at the beginning, it is well worth the effort, although going past Children of Dune is rapidly reaching the point of diminishing returns.
Oh, and Baal Houtham I’d recommend Steel Beach or Golden Globe for John Varley. The former is an exploration of News Media and AI Insanity with a sprinkling of Heinlein references, while the latter is an exploration of fame and con-artistry in the same universe. His new series Red Thunder, Red Lightning, Rolling Thunder is about the race to Mars and subsequent colonization apparently in a Heinlein-esque vein.
-DF
1- Adventures in Time and Space - I totally agree with everybody else. An excellent introduction to sf.
2- Either The Caves of Steel or The Gods Themselves or a short-story anthology by Isaac Asimov - I know some people dislike Asimov but he was a hero to me when I was a teenager. As he was my first science-fiction author I’m confident he can inspire love for the genre in others.
3- Rendezvous With Rama by Arthur C. Clarke - I may disagree with those that think Asimov isn’t a good author but I can understand where they’re coming from. Not so with Clarke whose books are not only well thought out but peppered with moments of beauty. I had to think very hard before chosing which book of his I’d select for my list. Runner-ups include 2010 and Songs of Distant Earth.
4- The Stars My Destination by Alfred Bester - People who dislike Asimov and Clarke are misguided, people who dislike Bester are crazy. It’s a thrilling book and a great introduction to space-opera.
5- To Marry Medusa or a best of anthology by Theodore Sturgeon - Sturgeon genuinely loved people and it shows. Also he was a bit more concerned with style than most of his contemporaries.
6- The Moat in Gods Eye by Larry Niven and Jerry Pournelle - An all around great book and the first on the list to truly focus on aliens. The sequel is not recommended, instead try out some of Larry Niven’s earlier works.
7- Dune by Frank Herbert - Again I can’t understand why there are people who dislike this one. Sure, it has faults, but its faults are shared by most science fiction and its better qualities set a high standard for the genre. Great, great example of world-building.
8- The Player of Games by Iain M. Banks - Not Banks’ best but still very good and his most accessible work IMO. Also serves as an introduction to the new space-opera.
9- Ring of Swords by Eleanor Arnanson - It’s accessible, original, thought provoking, funny and generally well-written. One of the very best examples of anthropological sf.
10- Ender’s Game by Orson Scott Card - It’s not one of my favorites but I felt I should put it in the list somewhere.
This was a tough one. I kept adding books and authors on the list only to take them out again as not accessible enough. Some of my favorite sf authors not only didn’t make it but never even had a chance (Greg Egan, for example). I know that the list isn’t very current but most of the newer stuff I read I think would scare the beginning reader away. Heinlein wasn’t included because I already had Clarke, Asimov, Bester and Sturgeon, all of whom I like much more. Also, I don’t think any book on this list except maybe The Player of Games or Ender’s Game is inappropriate for a young teenager but all of them are directed at an adult readership.