There's no denying that most of his plays contain some of the most lyrical use of the English language ever committed to paper. Phrases that he invented capture the truth of a situation with such timeless and classic beauty that they are still commonly in use today - A rose by any other name would still smell as sweet, etc.
But. For the large part, I could do without the sycophancy of the histories, and most of the comedies [apart from twelfth night] have aged badly. The old 'star crossed lovers/mistaken identity' thing that he did over and over is a bit hackneyed - obviously written to satisfy a contemporary audience, less delightful today.
The tragedies still pretty much rock face, though.
I consider him a good playwright whose works possess originality and eloquence, and there is no doubt how influential he is in the world of literature. I do, however, think it is difficult for many modern readers to get interested in his work, the Shakespearean style being so different from contemporary style.
Whether anyone finds him enjoyable or not is a matter of personal preference and there's no accounting for taste, but I suspect most people who don't like him either 1, don't get him AND were forced to read him (that's one composite reason), or 2, are superficially rebelling against his popularity/esteem in an effort to superficially appear nonconformist. I'm sure there are others who would not choose to read him, but I doubt he would inspire dislike if it wasn't for those 2 categories.
As for critical acclaim, I think most criticism is similar to the 2nd reason above: we can't allow anything to get by w/o some critique, so we nitpick. Among the critiques already expressed here, R&J allegedly "sucked"... but really only by comparison to some other faves. His comedies are dated... but really only in comparison to his tragedies (and what 300+ piece of writing isn't somewhat cumbersome?).
"...(and what 300+ **YEAR-OLD** piece of writing isn't somewhat cumbersome?)."
I don't mean to imply that Shakespeare is perfect or really even to refute the criticisms here, but considering how consistently popular and/or renowned he has been from his own lifetime onward, there just isn't much room to consider him a bad playwright. From the choices given, there's no way to justify "bad." Overrated? Perhaps, but not bad. While perhaps meritorious, criticisms of Shakespeare are ultimately equivalent to disparaging Cindy Crawford's beauty due to her mole.
Yes. That man actually invented words. Much of this material is still read to this day, may of his famous quotes are still recited. There have been recent movies and plays, and people actually study his work.