Read a book from each country in Europe.

And from Finland- Tove Janssons's 'Summer Book'.

From Monaco- 'Grace Kelly: Princesse du Cinema' written and edited by Richard and Danae Projetti (Stanislas Choko, 2007). There is a dearth of Monegasque literature sadly.

The poetry and writing of Lorca (Spain)

Cheating a bit but Frances Mayes 'A Year in Europe' is lit, architecture and cultural anecdote heavy AND she's a major Lorca fan but sadly is American.

AUSTRIA- (Spaltkopf) by the Russian-born Austrian writer Julya Rabinowich, published in English as Splithead by Portobello Books, London (2011). My Austrian friend recommends this.

AUSTRIA- Felix Salten wrote Bambi and his other major novel is called 'Josephine Mutzenbacher', the Viennese version of 'Fanny Hill' memoirs. It was published anonymously and was immediately banned by the authorities as being pornographic. The last 20 years have seen the novel rise to the status of a bestseller. So from Bambi to erotica in one Austrian writer!

The Expats is set in Luxembourg and gives a flavour of life there as an expat (though it's a spy novel).
When Hitler Stole Pink Rabbit is a great children's book set in Nazi Germany, France and England.

Georges Simenon was Belgian, though most of the Maigret books were set in Paris.

Italy - try History by Elsa Morante (though is set during the war). I read this a long time ago and noticed the other week that it had been republished.

Israel anything by Amo Oz or David Grossman. The Zig Zag Kid by the latter is particularly good.

Ireland no more than Human by Maura Laverty. This tells the story of an Irish nanny working in 30s Spain.

Perhaps something by Selma Lagerlof for Sweden? Am just about to embark on my first of hers, albeit in Easy Reader version as I am only just learning Swedish!

I've been thinking about this. I don't intend to do it as I seem to have a never-ending wish-list of books to read as it is, but if I were, this is what I'd do:

1. Do it in a structured way and give yourself exit points where you can stop and still congratulate yourself on your success. I'd define "Europe" based on EEC/EU membership over time (not a political judgement, just for convenience) so I'd probably start with the 12 "old" members:

Belgium, France, Germany, Italy, Luxembourg, Denmark, Netherlands, Ireland, Spain, Portugal, UK, Greece

Then, if I wanted to go on, I'd do: Austria, Finland, Sweden

Then:Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Slovakia, Slovenia, Malta and Cyprus

Then: Romania, Bulgaria, Croatia.

2. I think the secret is short books. If I were to attempt Don Quixote for Spain and Finnegan's Wake for Ireland, frankly, I know I'd never do it.

I'd start off with:

Italy: If on a Winter's Night by Calvino
Germany: Perfume by Susskind
France: The Library of Unrequited Love by Divry
Belgium: one of the Maigret books by Simenon
UK: a shortish classic I hadn't read (if you hadn't read Persuasion or Northanger Abbey by Austen, now's the time...)
Ireland: My Oedipus Complex and other Stories, O'Connor.

Read those six books - you mightn't like all of them, but they're all worth a go, and are quick reads with a strong "flavour" - and you can boast about being half-way through the first challenge.

For a light and fun read from Italy, any of the Montalbano detective books by Andrea Camilleri would fit the bill. Very different from the Scandinavian detectives, these are filled with food, sea and siestas.

I agree that Suite Francaise is compelling and sublime, but Nemirovsky was born in Kiev so I don't think she is really a French author for this project.

For a light and fun read from Italy, any of the Montalbano detective books by Andrea Camilleri would fit the bill. Very different from the Scandinavian detectives, these are filled with food, sea and siestas.

Can I recommend books by Fred Vargas - a French author. They are very good.
Etty Hillesum annoyed me.
Suite Francaise is a favourite of mine.It was heartbreaking to know that when her husband was writing letters to find out where she was, she had already been killed.

I have enjoyed several novels by Jose Saramago - Blindness was mentioned upthread, but The Double is also good (Portugal).

I recommend Where the Devil Can't Go By Anya Lipska ( Polish )

My DH, who loves a good literary challenge, points out that although Heinrich Harrer was Austrian, he was living in Liechtenstein when he wrote Seven Years In Tibet.

Try Italo Calvino's 'If on a winter's night a traveller' - a bit like Cloud Atlas in structure, unusual and engaging. Calvino was born in Cuba but lived in Italy all his life. For a topical WW1 theme All quiet on the western front by Erich Maria Remarque is very poignant, told from the German point of view of a young man at the front. France: Bonjour Tristesse by Francoise Sagan is a short but great easy read.

Cees Nooteboom has been mentioned and I second that, he's Dutch.
Harry Mulish is also Dutch and not Belgian.
Dmitri Verhulst is Belgian, and has been translated.

I forgot two

Ukraine -

Pengin Lost by Andrey Kurkov. Satire about life in post-Soviet Ukraine and so, so hilarious. The follow up, Death and the Penguin is a lot darker.

Serbia

In the Hold, by Vladimir Arsenijevic, about life of disaffected youth in Serbia after the war.

And Norway: Kristin Lavransdatter by Sigrid Unset, a real masterpiece

The Master and Margarita by Mikhail Bulgakov (Russia)
The Heart of a Dog
The White Guard or anything else by Bulgakov

A biography: Pushkin's button by Serena Vitale

Poetry: Anna Akhmatova, Marina Tsvetaeva

as for the Italian literature, The Garden of the Finzi-Continis by Giorgio Bassani is most beautiful.

What a great idea!

For Denmark/Greenland, how about Miss Smilla's Feeling For Snow by Peter Hoeg (can't do the slash through the 'o'). Lots about the relationship between Denmark and Greenland; very interesting.

Sadly, A Short History of Tractors in Ukrainian is set in Peterborough. But amusing for all that

I can heartily recommend the following;
Spain - The Carpenters Pencil by Manuel Rivas. He is amazing.
Germany - Austerlitz by W.G Sebald.
Russia - Summer in Baden-Baden by Leonid Tsypkin

From Iceland you might like "The Greenhouse" by A A Olafsdottir, which I enjoyed a lot, also I see it is in the Kindle May promotion for just £1.

According to wikipedia, Juli Minoves Triquell and Josep Carles Laínez are both authors from Andorra. Finding their work in English might be some challenge, though. Also, Laínez is actually Spanish, I think, just lives in Andorra.