Great suggestions especially as I'm just coming to the end of Anna Karenina and loving it. The other Russian novel which I would recommend is Dr Zhivago.
My list would also include:-

Brideshead Revisited
To Kill a Mockingbird
The Grapes of Wrath
Midnight's Children (surely already regarded as a classic)
Goodbye to all That (not a novel, I know but essential reading)
1984 (I'm suprised this hasn't already been mentioned!)

One of my reading resolutions for 2009 is to read another Russian classic possibly 'Crime and Punishment' or the Brother's Karamazov.

Happy Reading New Year, everyone