It all depends on the context it's used in. Often, "Paki" is used to refer to anyone of South Asian appearance, and I don't know if everyone's totally aware of this, but not every nation in that region exactly sees eye-to-eye, and that animosity is bitter enough for some people to be offended when incorrectly referred to as being from Pakistan. For example, there are a fair few Indians who would be a little pissed off if you called them a Paki. Even if you don't intend to use it as a slur, quite often it might taken as such.
Regional tensions aside, referring to all people of a certain skin tone as being of the same background is pretty racist, which is exactly what a lot of people who use the term Paki regularly do. My stance - just don't fucking use the word.
Terms like Brit, Aussie, and Yankee are a different matter. In my experience, they're usually used simply as an abbreviation for the nationality to which they refer. I assume they're all used in a derogatory manner sometimes (I know Brit and Yankee are, not sure about Aussie), but again, context. Context is king.
Captcha: glazed donut. That would be amazing, Escapist, fucking amazing.