Asimov's Robot series as well, try and get "The Complete Robot", it's about £6 from at least one retailer and is a good read and introduction to his writing (iirc it's got all his short Robot stories in publication order, combining the I robot and Rest of the Robots along with a number of other shorts that hadn't been collected together before).
Possibly some of the Skylark series by E.E. "Doc" Smith (iirc written in the 30's) if you want something from that far back.
The Complete Arthur C Clarke has some gems in it (it's all his short stories, including some that are only a page or two long*).
2001 and the sequals.
H.G. Wells, War of the worlds etc.
Jules Verne - 20,000 leagues under the sea, From Earth to the Moon etc.
Personally, if you're new to science fiction i'd probably take it easy and try some of the short stories by various authors to get a feel for who you might like, then try some of their longer stories and work from there (jumping straight into something like the Nights Dawn Trilogy is probably a bit of a plunge**)
Robert Heinlein's -Stranger in a Strange Land, Starship Troopers (the original story the film is based very loosely on.
Larry Niven's Ringworld (then move onto the sequels, and then the extended universe surrounding them).
Frank Herbert's Dune, then the sequels.
I'm currently trying to read (or in some case reread) some of the early Science Fiction stories, such as the Skylark series, 20,000 leagues under the sea etc, as it can be fun to read some of the really old stuff, not to mention a number of authors make discrete refereces to the older stuff (or simply other authors).
*One of my favourites from it is basically an excuse for the pun at the end.
**I say this as someone who really enjoys Hamilton's books (and indeed have most of them on my shelf).