I'm planning to move out, hopefully sometime during august, and never see or speak with my family again. Are there any legal obligations I might have towards them or any special privileges they might have? For example, could I be named their guardian or have to pay off their debt or could they do anything to track me down? Things like that, anything that would legally differentiate them from a random stranger even though I'm an adult and wouldn't be living with them.

Only thing I can think of is you might be called upon to identify them at a morgue........

But remember that it applies retroactively as well, they won't help you if you don't help them.

could I be named their guardian or have to pay off their debt
Debts cannot be transfered from person to person. If they die, all debt vanishes (of course if they die in debt it means you don't get left any money).
or could they do anything to track me down?
Sure, there's nothing illegal or odd about that. Anyone can pay to track anyone else down, regardless if they're related or not.
anything that would legally differentiate them from a random stranger
If you die and they're your closest living relatives and you don't have a will, then they get everything. Other then that, not much. You could technically disown them or legally change your name, but its really not worth the hassle. Just move out and be done with it.
Only thing I can think of is you might be called upon to identify them at a morgue........
You can't be legally forced to identify a body at a morgue

You can't be legally forced to identify a body at a morgue

Hence why he said "might be called upon" rather than "legally forced to".

Hence why he said "might be called upon" rather than "legally forced to".

Then there's no point in mentioning it really

"Any legal obligations to your family?"
"Well, you might have to get them a birthday present"

pretty much the same thing as "you might have to identify them"

If they have any assets at all, you probably shouldn't make such a fuss. Just leave. You might as well get their assets when they die rather than the state.