This was my first introduction to his collected short stories, and it had an enormous impact on me. I think my favourites are 'Thanasphere', which was wonderfully eerie, 'Der Arme Dolmetscher', which had you glued to the page, and 'The Package', which evokes just about every emotion you've got, from pride to elation to guilt and crippling sorrow. I'd recommend this endlessly to people who either have never read Vonnegut before, or have only read his full-size novels.
I've read a couple of his novels, and thoroughly enjoyed them, but there's something about the bite-size stories in this collection that are just the right about for a serving of bliss. He even talks about the effect a short story can have on a person in his introduction - a sort of "Buddhist cat-nap". You'll love it, I promise.