Right now (until August 12th) you can vote on NPR's list for the 100 top Sci-fi and Fantasy novels of all time. I've put mine in, and while there are several deserving candidates that I didn't vote for (like Tolkein won't make the list if I don't vote for him), these are my choices. I didn't vote for cultural significance. I voted for things that spiked across my brain in the right way, and have mattered to me.
1. Watership Down, Richard Adams
This is probably my favorite book of all time. Great adventure, vibrant characters, clever use of myth and storytelling within the story. And you know what else it is? It's a great heist/prison break story. And an epic war story. The fact that it's rabbits is almost incidental.
2. Lillith's Brood, Octavia Butler
This trilogy is really fantastic stuff. Humanity is saved from their own self-destruction by aliens-- aliens that turn out essentially be a kinder, gentler organic Borg who insist on "trading" DNA with the surviving humans-- and those humans are none too happy about it. Told from the perspective of Lilith-- the first human awoken after the cataclysm, who is forced to accept the terrible reality of the future of the human race, and sell it to the rest of humanity. Great stuff.
3. Parable of the Sower, Octavia Butler
Octavia Butler is the only repeat on my list, which came to me as a bit of a surprise-- but it shouldn't be TOO surprising, because she was a fantastic writer. The Parable duology (actual Parable of the Sower and Parable of the Talents) is a frightening look at the near future. Not dystopian, but close to it, as it shows an America falling slowly into anarchy as government gets weaker and weaker and gives more and more to privatization, and the middle class has completely crumbled. Scary, prescient and fantastic.
4. Moon is a Harsh Mistress, Robert Heinlein
Probably my favorite of the Heinlein, possibly because it it's solid, dynamic, and minimizes the somewhat creepy group-sex aspect that seeps into many of his works. Especially his later works. Moon, however, has little of that, and plenty of great worldbuilding and fun action.
5. Lies of Locke Lamora, Scott Lynch
Really fun caper, old school fantasy written in a modern voice. I will admit a certain degree of over fondness for a book that's probably too new to really belong on an "all time" list... but I don't care. It's fun.
6. A Journey to the Center of the Earth, Jules Verne
Some serious old school to balance the previous recent work. When it comes to old school, I'm a big fan of Verne over Wells. Journey was one I read and re-read many times as a teenager. My old copy is on my son's shelf, beat all to hell.
7. Hitchhiker's Guide to the Galaxy, Douglas Adams
Yeah, like this one wasn't going to make my list.
8. Foundation Trilogy, Isaac Asimov
Or this. Seriously, Asimov and Adams were a major part of my teenage reading.
9. Anathem, Neal Stephenson
Just about all of Stephenson's body of work is on the nominating list, save my personal favorite of his, which is Zodiac. But Anathem is a close second for me. It's a solid, clever story that moves, and once you get into the groove of the made-up vocabulary, the worldbuilding really sings. Plus it has an ending that's a proper ending. I like that in my novels.
10. Belgariad, David Eddings
Yeah, it's more sentiment than true value, but it's a series that has always been important to me. So of course I'm going to include it. And, like I said, it's not like Lord of the Rings needs my vote.