There is one small problem with classics though: they may contain old words. However, a 10 year old book may also contain “old” words, so that lazy argument is rather pointless. In case you are going to read Swedish books (in Swedish) from the early 19th century, you may have some issues with old spelling, plural verb conjugations and other things, but for French, English and Russian, the differences aren't very big. And if you read a modern translation of an English classic (for example), you aren’t that likely to run into ancient spelling.
There is, however, another issue to take into consideration. Classics are classics because they weren't written last year and because they had an impact on the readers, on the society, of their time. Jane Eyre may not seem very outrageous today, but it was in the middle of the 19th century. In order to fully enjoy stories that deal with society, it is often a good idea to read up on the historical context while reading. Or if that is too much trouble, you can just state that “naah, the book was boring”. Classic books can be a bit slow, especially if your primary source of culture is 1,5h long movies where everything happens incredibly fast. For anyone used to reading, it shouldn't be a big deal though.
French classics very often have sections at the end of the book that explain concepts, symbolisms, etc., and those should definitely not be overlooked. I think my reading of Le Cid would have been partly pointless without the notes that accompanied it. Some books do just fine on their own and people read and enjoy them no matter what their previous level of knowledge is, but I think a large number of classics improve significantly if you try to go back a bit in time.
Some awesome classics:
Pär Lagerkvist – Barabbas (the first book I read in French)
Hjalmar Söderberg – Doktor Glas
Victoria Benedictsson – Pengar
Beaumarchais – Le Mariage de Figaro
Choderlos de Laclos – Les Liaisons Dangereuses
Guy de Maupassant – His short stories
Emily Brontë – Wuthering Heights
Jane Austen – Pride & Prejudice
Charles Dickens – A Christmas Carol
Feodor Dostoevsky – The Idiot
Mikhail Bulgakov – The Master and Margarita
Chekov – His short stories
I haven't read enough Norwegian classics to be able to recommend any, and for the above languages that's just a small selection. What are your favourite classics?