I don't know this thread existed till now, so here are my remarks. (I did wrote about the Nobel Committee's decisions between 1901--1939, so you can check the reasons for their selections).
As for recommendations:
Sully Prudhomme: read some of his poems, not bad, but not extraordinary. Very difficult to find any of his volumes, but the Committee listed Stanzas and Variations. If you can find it, good luck. For me, just like Hayden said, a terrible mistake. Zola all the way.
Bjorson: read few poems. Not his greatest works, that should be his dramas and novels (unfortunately haven't read them). Based on descriptions from the Committee, his plays are social issued themes with realistic touches like Ibsen (both were shortlisted in 1903). I will read him so I can judge if he's better than Ibsen.
Frederic Mistral: read Mireio and Memoirs on Project Gutenberg few years ago. Again, didn't enjoy the former but the later was good, so I think Memoirs should be the starting point. For me, not a great candidate. Maybe George Meredith could have prevailed.
Henryk Sienkiewicz: read Quo Vadis, one of the best novels from 19th Century IMHO. The greatest achievement in the book is Sienkiewicz's great descriptions of the fire setting ablaze the church, a scandalous act ordered by Nero for the sake of poetic inspiration. Another highlight is when Peter was running away and Jesus appearing to him and telling him to go back to Rome, this was during the persecution of the church. Great novel. The Committee mentioned Jakob the Musician and Trilogy of his historical novels as high points, but I haven't read those yet. He might not be better than Tolstoy (who was dismissed for scandalous work in Kreutzer Sonata), but I think he's one of the best choices the Committee made in that decade.
Carducci: read Barbarian Odes. Issues I have about him is that some of the poems seems to remote and distant (that's his poems are historical, if you're not Italian, you can't understand what the poems are about). But the best of Carducci is in his philosophical poems like Diaptheria, At the Station. He's very innovative especially in his application of colours, that's impressionism. I think based on the shortlist for that year, he's worthy choice. He needs a modern translation.
Kipling: read Kim, Jungle Books, Captain Courageous and few of his poems. Please, people shouldn't bother with his poems, just read Kim, his best novel, and Jungle Books, for children at least. Capt Courageous wasn't that bad.
Eucken: read few essays, not his entire volume yet. He's not a philosopher per we, because he doesn't engage the reader in an intellectual discourse. I would say he's more of religious writer. Not really a bad choice, but I think he was a compromise choice, for the Committee was divided between Swinburne and Lagerolf.
Lagerolf: read Wonderful Adentures of Nils. Great book for children. I haven't read her more famous works: Jerusalem and Gosta Berlings Saga. I feel Lagerolf and Sienkiewicz are the best from this decade.
Maeterlinck: a great dramatist, one of the most under-rated. A symbolist dramatist/poet who predicted Waiting For Godot nearly half a century later in his masterpiece The Blind. His poems, which one can find in Project Gutenberg, is very reminiscent of Baudelaire and Verlaine. Great choice even though a titan like Henry James was shortlisted the same year. Recommend Maeterlinck to lovers of great literature.
Tagore: read few poems (Selected Poems) very romantic in tone, which displays the influences of Keats and Tennyson. Haven't read his novels and short stories yet. One can enjoy the poems, but I didn't.
Romain Rolland: read the first two volumes of Jean Christophe (very beautiful). I did tried to read Tolstoy, his biography, but couldn't finish them. His other books like Soul Enchanted and Beethoven can be found on Project Gutenberg. I haven't read Benito Perez Galdos, who was shortlisted with him so I can't judge.
Knut Hamsun: read Hunger and Pan. Wholly recommend. He's one of the giants.
Bernard Shaw: one of the greatest dramatists out there, very social playwright. Read Arms and the Man, Pygmalion, Man and Superman and Back to Methuselah. One should read the first three before trying the latter. Great choice.
Yeats: one of the finest poets of the last 100 years, a great choice even though he was shortlisted with great Thomas Hardy. Read his Collected Poems or try in individual volumes Michael Robartes, Winding Stair or The Tower.
Henri Bergson: one of my favourite philosophers, I wholly recommend Time and Free Will.
Thomas Mann: I think everyone here has read him. But for those who haven't, try Death in Venice, Magic Mountain, or my favorite Doctor Faustus. One of the best novelist in any language.
Sinclair Lewis: read Babbitt, Elmer Gantry and Dodsworth. Very surprised few people read him these days. Recommend the first two before the last one.
Pirandello: read Six Characters in Search of an Author. Very innovative play. Highly recommend. I will try and look for his other works.
Eugene O'Neill: a master of drama known for his expressionistic approach influenced by Strindberg and realism of Ibsen and Shaw, read Long Day's Journey into Night and Anne Christie. Recommend both works.
Du Gard: read the first two volumes of The Thibaults, recommend it.
Silanpaa: very unfortunate few people hav read him. I read People in the Summer Night and was impressed in it's polyphonic and existential vision. If I can see more of his books, I will definitely read him. Recommend People in the Summer Night.
— I've read a fair handful of Prudhomme's poetry... he's okay ?
— nothing exciting.