it depends on what info you really what to know. i work in an hla typing lab and everyone here has their dna on file. we went as far as allele typing and knowing what part of the world the allele is most prominant. for ex. i have allele's that is most commom in people of asian decent. i also have an allele that is prominate in people of medditeraan decent.
but you can go ay furhter theis this and get you dna sequenced and all that good stuff. while the lab im at can do this, we dont because that is not our main focus or job. we just do the allele thing for the fun of it.
if you want to find out if you are related to some famous person, there are labs that will do that. just make sure its legit. dna testing is expensive. the things we do is 5000$/sample and it is not by any means in depth as you may want to go.
i'm actually at work right now trying to save lives, so i cant get into as many details as i would like, but will try to reply back later if someone else hasnt chimed in already.