I've never sat down and read it from beginning to end. However, I have grappled with it on and off over the years, dipping in and out, reading and then re-reading certain chapters, and so on. So overall I'd say I've read it (sort of).
Parts are undeniably beautiful. Think of the rays of sunlight criss-crossing in the martello tower, or the wandering rocks chapter, or that orgasmic description of the sunset in Gibraltar. Joyce had an astonishing 'mimetic power', as I believe it's called, meaning an ability to make the word the thing. Read his description of a dog running across a beach, for example, or Molly turning over in bed to drink the tea that Bloom brings her. It is so vividly there in front of you.
Do I enjoy Ulysses? Hand on my heart? Hmm...parts of it. I really like the opening five chapters, and the wandering rocks bit, and also the burial scene. Parts of Molly's monologue are wonderful too. But it's just too long. It's also, dare I say it, really f-ing boring in places. Martin Amis said that "the stream of consciousness is a bore," and there was a great gasp of joy from the audience when he did. A lot of people secretly feel that way, but keep quiet for fear of being thought stupid. Many of Bloom's thoughts just aren't interesting. I mean, compare Bloom's interior monologue to the thrilling ideas that spark off the page in an Aldous Huxley novel, or Wilde's Dorian Gray. Then again, I suppose that's the point. Ian McEwan chose Ulysses as his desert island book because, he said, it perfectly captures a day in the life of an ordinary, flawed, but fundamentally decent human being. And when you read it, you are fully in that world – outside of space and time. Ordinary life is mundane and boring.
Joyce was a superb writer, that I don't doubt. Dubliners, in particular, is a masterclass in the short story. Indeed, parts of his work are breathtaking (think of the snow scene in The Dead). But he's really difficult, there's no getting around it. He's also, to some extent, parochial. He is preoccupied with catholicism and nationalism – the two big isms for an Irish writer. Parochial British writers, on the other hand, tend to be obsessed with class (E. M. Forster, Evelyn Waugh, Alan Bennett, etc). And even those who aren't interested in class still seem class-bound (Aldous Huxley, Anthony Powell, Jane Austen).
If you want to grasp the Joyce genius, read Anthony Burgess. Burgess was a disciple of Joyce and knew his work inside out. But he's more accessible somehow. I get from Burgess what other people get from Joyce – language used in thrilling and extraordinary ways. He's a great way into Ulysses. I just wish I enjoyed reading Joyce as much.