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.
In a related question, [Can you compile C# without using the .Net framework?](https://stackoverflow.com/questions/551554/can-you-compile-c-without-using-the-net-framework), it's mentioned you could do this using mkbundle from mono. I haven't tried it myself so I can't comment on if it's the way you should go, but you may want to consider it.