Actually, " Buy me ice cream" and "Buy me an ice cream" are both correct. In the first statement, "Buy me ice cream", you are simply asking for ice cream in general, no specific amount is asked for. So the person buying ice cream will come back with whatever amount they feel is correct. In the second statement, "Buy me an ice cream" you are asking for a single serving of ice cream, and it would come in a cup or cone. Now, Julia is right, a please at the end in either sentence is more polite. Also, in the complex world of ice cream, I assume the person knows what flavor you want. I hope they know what flavor I want too, because ice cream sounds like a good idea!

Buy me an icecream, please! ;-)

Buy me ice cream please! (two words)