Question: I want to develop a small utility for windows and I prefer doing that in c# because it is easier (I'm a java developer). 

The utility will be available for download by many people and I assume some of them will not have the .net framework installed (is this assumption correct, say I target win xp and above?)

My question is: can a c# application be compiled in a way that it will not require the .net framework installed?

Answer: 
No, it will need the .Net framework installed. Note though that you will need only the redistributable version, not the SDK.
You can probably also include the .net framework installer in your application.