Any suggestions for books you HAVE to read are more than welcome. Any subject.
If you haven't read many classics, or even much fiction in general, I'd make sure to start with something accessible. I'll add another vote for To Kill a Mockingbird. Here's some others, all of which should ease you in. Just read the first page of each (either in store or on Amazon) and go with whichever one draws you in the most.
The Great Gatsby - Probably the only 20th century novel whose reputation eclipses Mockingbird. Less "sincere" than that, but it definitely has it's dark parts.
The Catcher in the Rye - Seems to be either a life-changing book or one people disregard with a shrug. I still find it endlessly entertaining, funny and poignant.
The Big Sleep - This veers more into the crime genre than literary fiction, but it's a classic nonetheless. So tightly written. Not a single wasted sentence.
On The Road - With it's rambling style it may come across a little complex at first but don't take it too seriously. Just get lost in the rhythm and don't worry if you're "getting it" or not.
The Grapes of Wrath - Very powerful book and again easy to read, but considerably longer than the rest.