Restaurants are aplenty in Dubai. Dubai is truly a melting pot of different cultures with cuisines like Chinese, Thai, Indian, Italian, Arabian and several more. It gives a real taste of Asia.
Below are some of the best restaurants in Dubai:

Thai Restaurants:

The Benjarong restaurant has got to be the best Thai restaurant in Dubai. It is situated in the Dusit hotel and offers a fantastic view of the desert. The food is served piping hot and has the traditional authentic Thai taste.
But close follows the Blue Elephant. Though I have not personally visited this restaurant, its reputation is clear proof of the great food that is served there. The Blue Elephant hs tasted success in London and is looking to repeat the same here in Dubai.

Italian Restaurants:

My choice would be the La Vigne restaurant in Century Village. It is one of the best Italian restaurants that I have ever dined in. Though there is the Cappa Nuovo and the Venezia restaurant, my personal favorite is the La Vigne. The food is reasonably priced. The ambience is not something out of the world but the food is simply awesome. So be sure to visit this restaurant while at Dubai.

Indian Restaurants:

Indian cuisine is one of the most widely avaiable in Dubai. To begin with, visit the Saravana Bhavan or Sangeethas (both are located within 100 metres of each other) for breakfast. They offer excellent South Indian delicacies, all served piping hot.
For lunch, try the Sukh Sagar (situated in Al Karama) or the Gazebo. These 2 restaurants offer very good North Indian food. Apart from these, there are several other joints like the Bombay Chowpati chaat joint which has awesome Indian chaat ( chaat is something like a street snack in India and Bombay Chowpati totally rocks in this division ). So if you are looking for Indian food, head to these restaurants.

Chinese Cuisine:
Dubai has too many Chinese restaurants to list out. Though I have been only to the Golden Dragon and the Chinese Kitchen, there are several other options. These restaurants offer quality chinese food at affordable rates and are the apt choice to get a taste of Chinese street food. Every area in Dubai has atleast 2 Chinese restaurants. So wherever you are staying, you will never be far away from a Chinese restaurant.

Arabian:
I think Arabian restaurants would be only too easy to find Dubai! So there would be no use of me posting their names here.

I think the above list of restaurants is far far away from exhaustive. These are just some restaurants that top my favorites list. So if you are an adventurer, go ahead and visit the many other restaurants in Dubai.Enjoy!