I've lived in Rochester for 20 years, and in my humble opinion, The King and I is the best of the vegan-friendly restaurants in Rochester. Most dishes at this Thai restaurant is made with a wonderful variety of vegetables cooked to perfection, and the sauces are delicious. The food is served very promptly and the service is terrific.
My personal favorite is the eggplant vegetable, while my boyfriend and a good friend can't get enough of the evil jungle. The phat thai is also excellent. Other favorites include the ginger, the cashew, the panang curry, the phat phet, the spicy veggie, and I could go on and on. While I do agree with the previous poster that the sesame tofu is good, I actually think it's a bit too sweet, and it doesn't come with much in the way of vegetables, just fried tofu, broccoli, and a sweet sesame curry sauce, so, even though it's quite good, I actually don't get it very often.
The soups at The King and I are also good (we especially like the Tom Kar coconut soup) and so is the Som Tom (papaya salad) which can be made without fish sauce on request. The only thing I haven't been that impressed with are the spring rolls, which are okay, just not as great as everything else. Overall though, the restaurant is excellent, and the first place I would recommend that a vegetarian or vegan coming to Rochester should try.