So so many!
For Indian/ Pakistani you have everything from the cafes of Satwa (Ravi's has a great reputation for good food at cheap prices, though you can't really go wrong) to high end Indego by Vineet at Grosvenor House.
Italian - Bice at Hilton Jumeirah at high end, Jamie Oliver has opened a new Italian restaurant in Festival City at good prices (US$15 a main), Bussola at Mina Seyahi though book upstairs for the al fresco pizzeria as better than the a la carte downstairs.
Best restaurant in Dubai is Reflets par Pierre Gagnaire - it's VERY expensive in the evening (but worth every penny) but they also do a lunch offer of 3 courses for AED180 (about $50) - not many places you can get 3 star Michelen French food for that price.
http://www.timeoutdubai.com/restaurants-awards-2010 can give you the full lowdown