A good read?

I really enjoyed The Full English. Good humour and, for once, just nice low key cycling that most can relate to. I also liked the 2 books about the Tour and Giro, second was called Gironimo.
Finally, the Man who cycled the world book was good but the follow up about riding across the states was just pish.

The Greatest Cycling Book Ever is universally and unquestionably accepted as...
The Rider, by Tim Krabbe.

It's a novel (hardly more than a short story really) but it captures the soul and essence of cycling and racing like no other, in beautiful sparse writing.

Having said that, all very good suggestions from @crikey and @otis .

Domestique (Wegelius) and Dog in a Hat (Parkin) are great reads if you want a look at the less glamorous end of cycling, not the star performers. Jean Bobet is also good because it is so personal, and Michael Hutchinson writes very well.

You could also look at the Sean Yates book, It's All About The Bike, which avoids doping completely but is somehow still an honest book. Sean Kelly's book I found disappointing - much more of a ghost-written list of rides and anecdotes.

Laurent Fignon's autobiography is refreshingly honest and a excellent read. It's ashamed he is often erased from cycling history because he admitted to pre EPO doping in the form of cortisone, simply because he didn't reamain silent like the others pre modern era.

"Rough Ride" by Paul Kimmage. It was the William Hill Sportsbook of the Year in 1990. I find it even more interesting to read it nowadays in contrast to how things have changed over the last 20-odd years. Different world.

I think that the Cycling Anthology series have been brilliant (the fifth one was just released a couple of weeks ago)- they combine a wide range of topics and angles as well as bringing together some great writers. Otherwise my personal favourite is Jean Bobet's biography of his brother Louison, "Tomorrow We Ride" simply because of the style and use of language. The shelves on by bookcase are literally bending under the weight of the wide range of books available- one thing that cycling has in common with boxing is that they provide the best sports writing available. I also find Ned Boulting's books very funny and very readable- in fact he released an e-book recently about this year's TdF and I read it in 2 sittings. If you are looking any more suggestions try and focus on an area of interest at a time otherwise it will be very overwhelming.
I can add some suggestions while avoiding repeating any already mentioned- Slaying the Badger (the story of the 1986 TdF) by Richard Moore;
Etape (an slightly different look at the Tour throughout history, again by Richard Moore);
The Death of Marco Pantani by Matt Rendell (I also recommend the DVD based on it, The Accidental Death of a Cyclist);
Marco Pinnotti's "The Cycling Professor" (still only available on e-book as far as I know-part autobiography, part science lesson);
Michael Hutchinson's "The Hour" is funny but informative about his attempt on the Hour record and his recent book "Faster" also manages to make the science behind riding a bike readable.

These are just a few of the top of my head but I don't think you would go far wrong with the Cycling Anthology series I mentioned at the start since they cover so many writers that you can get a taster and see who you would like to read more from- that way you could develop your own reading list.

If you want to read about cycling, it's best to accept that a single book will not really suffice.
One of the really interesting things about cycling is the sense of history and tradition... (as appropriated by some modern cycling clothing companies to sell over priced clothing...), so aim to read around the subject to develop a sense of what happened and why it happened.

Try these:
Bicycle Road Racing by Eddie Borysewicz
Complete book of Cycling by Chris Boardman
It's not about the bike By Lance Armstrong
One more Kilometre and we're in the showers by Tim Hilton
Bikie by Charlie Woods
Slaying the Badger by Richard Moore
Bad Blood by Jeremy Whittle
Obsessive Compulsive Cycling Disorder by Dave Barter
Racing Through The Dark by David Millar
The Secret Race by Tyler Hamilton
Inside the Peloton By Nicholas Roche
Domestique by Charly Wegelius
A Dog In a Hat by Joe Parkin
We were Young and Carefree by Laurent Fignon

Some are modern 'sports biographies', some are gritty confessions, some are just good reads, some are lies. All will contribute to an understanding of how and why cycling developed the way it did, and may in turn delight, inspire and disillusion you.

I'm currently reading Richard Moore's In Search of Robert Millar.

Biographical stuff tends to bore me but Millar was just such an incredibly challenging character to understand.

I'm only 27 so I don't have any first hand experience of the 80's era but it's my favourite to learn about by far. On that note, Slaying the Badger is fantastic too.