Actually it's pronounced three ways, nēsh, nich or nish, and I would prefer to pronounce it like the British and French.
dictionary.com is based on Random House's dictionary, an American dictionary (as is Merriam-Webster) and they both put nich first. Oxford, on the other hand (the recognized authority on the English language), puts nēsh first.
Unfortunately Americans have a nasty habit of butchering the spoken word. In Britain (you know, where the English language originated) it's nēsh, as it is in France where the word originated.
Now, you can go on speaking like an ignorant American, or you can speak like a truly educated worldly individual like Matt Cutts.
