My Father's Dragon, Charlie and the Chocolate Factory, the Magic Faraway Tree trilogy, Paddington have all gone down well with DS, who will be 4 soon. The biggest problem I'm finding with picking chapter books, is being sure the themes aren't too mature/upsetting for age 3/4 (and especially that nobody dies!)
I know you asked for a non picture book but have you seen the Usborne beginner books, they're a range of information books which are very cheap second hand on amazon. They are great for introducing nonfiction books and make a change from stories every night. There's a whole range of topics, they have chapters so you can read one a night. My 4yo ds likes to choose a chapter to read together. His current favourite book is called Bugs. (I don't work for Usborne but do love their books!)
Flat Stanley is good - and if he likes them there are lots of them now. Roald Dahl also fun to read but I would avoid The Witches and The BFG unless you have a fairly robust four year old. Winnie-the-Pooh is nice for this age, and possibly even The Wind in the Willows. Pippi Longstocking and My Naughty Little Sister also went down well at four and are nice and gentle for bedtimes.
Pippi Longstocking Jolly Rogers (Johnny Duddle) Dixie O'Day by Shirley Hughes and Claire Vuillamy Claude by Alex T Smith Percy The Park Keeper (blimey, just realised I haven't read those for a long time, sniff) My Naughty Little Sister Lotta Says No The Alan Ahlberg Happy Families series Parrot Park by Mary Murphy
Ive just bought Tom fletchers The Creakers to read to mine at bedtime which we will give as a Christmas present. Ive also preordered his Christmasaurus which we will be reading a chapter a night through December as sort of an advent calendar type thing.