I. space travel (and overall winner)
This is the easiest (and the only one whose name we know). The person who covered the longest distance during his lifetime has to be Sergei Krikaljow:
Krikaljow spent a total of 803 days in space, constantly circling the earth. There is no number given in the Wikipedia article, but the previous record holder, Sergei Avdeyev ( https://en.wikipedia.org/wiki/Sergei_Avdeyev ) spent 748 days in space, covering no less than 515,000,000 kilometers. Mr. Krikaljow has significantly more miles under his belt.
II. air travel
This has to be a cabin crew member (less likely a pilot) who: (a) works for a commercial airline in North America and (b) has a long and uninterrupted career.
So I would go for a 65 year old flight attendant from Atlanta, GA who started her job in 1965 and has worked full time ever since, flying from Boston to Los Angeles, from Chicago to Miami or from New York to London on an almost daily basis for decades.
III. motor vehicle (land)
This has to be a professional truck driver in North America. The USA and Canada have a large and well-maintained long distance road system which can be used basically during all 4 seasons of the year (as opposed to, let’s say, Siberia).
My choice: A 70 year old truck driver from Wichita, KA, who started driving all over the USA and Canada full time in 1960 and is still working in his job.
IV. ship or boat
This has to be a seaman on a modern day container vessel with a long and uninterrupted career.
My choice: A 65 year old machinist from the Philippines who has been a seaman working on merchant vessels all over the world since 1962.
I go for an ancient Mongolian warrior who rode from the steppes of Mongolia to Poland and back.
VI. walking and/or running
I don’t know where to start: A mail runner in the ancient Inca empire? A hunter in Africa or Australia? A Roman soldier who was stationed in Britain, in Germany, in North Africa, in Asia Minor, in Spain and on the Balkans during a 40 year career and walked every single mile?
Or maybe a modern day fitness buff who took up extreme long distance running when he was 16 years old and is still training like a maniac every single day at age 70? This is probably not an absolute top athlete, but rather a very dedicated amateur who has never really cut back on his training schedule as he got older.
A modern era competitive swimmer (maybe from the Eastern Bloc some decades ago) who swims 10 kilometers or more (I’m guessing) every day.