THIS is a good list of "must read" books. There are a lot of safe picks here, such as "To Kill a Mockingbird" and "1984". There are also some good picks that often go overlooked on lists such as this. "The Lords of the Rings Trilogy" being an example.
It's almost impossible to narrow down a list of "must read" books to only 30 entries. There are literally hundreds that I would have to start with. My list might have a few more Sci-Fi picks. "The Foundation", "Dune", and "The Moon is a Harsh Mistress" are all great literature, despite being too often labeled as nerd books.
I'd also take "Walden" off that list. It's d u l l. Really, really dull. And the themes are not terribly compelling. And although "The Origin of Species" is a masterwork that has had more impact on mankind that anything else on that list, it's non-fiction, written in an 18th Century dialect, and is very hard to get through. I'm a big science nerd and used to spend time on the internet "debating" evolution, and I couldn't get through it all. Be warned.