As Nix says Asimov, Phillip k Dick and Orson Scott Card all have good books for people who want to try reading something different for the first time
I'd highly recommend Asimov's Caves of Steel for example, as both science fiction, and detective

Or his Robot shorts to get a feel for him.
Some of Heinlen's books are still very good even today (although his later ones are not as good a lot of the time, and his attitude towards women isn't PC

).
Puppet Masters for example is a classic alien invasion story and has (from memory) been made into films twice officially (and I think several more have been based on a very similar idea), and "Stranger in a Strange Land" and "The Moon is a harsh mistress" are both fairly classic.
Larry Niven's Ringworld series is a must if you try some science fiction (in my mind), it's one of the series that I tend to reread every few years, indeed I'm currently reading as much of the "known space" and "man kzin wars" books and stories as I can find at the moment (the Ringworld takes place in the "Known space" universe after the Man Kzin Wars, but you can read Ringworld blind).
In addition to the above David Weber's Honor Harrington series are good, the first few are available as free ebooks from the
Baen free library (and if you like them you can buy an ebook bundle with the whole series + more for about $12*), very nice if you've got a Kindle or other ebook reader (and played a very large part in my decision to buy a Sony PRS 505 a couple of years back).
Basically space opera in the vein of Hornblower (I think), but in Space
Peter F Hamilton's Pandora's Star and Judas Unchained are are a very good SF series, but long at something like 1000 pages each (and the Void trilogy that follows on as a sequel series is another ~3000 pages)
Dune is to my mind a great book, and a good series of books (at least the ones written by the original author), but can be very heavy going at times from memory.
For non Science Fiction/Fantasy stuff, one of the obvious suggestions is Tom Clancy's "Ryan" series, starting with The Hunt for Red October.
*I think the July 2010 set has the 4 books including the latest in the HH series, and also includes a CD image with about 30+ more ebooks (the whole HH series up to the latest one).