…in their lifetime?
Taxi drivers? Long-haul truckers?
A commercial airline pilot/crew? They log hundreds of miles every single day for potentially many decades.
Astronauts? Those who travelled to the moon got a half million miles in one shot.
Valeri Polyakov was on Mir for almost 2 years (total, over 2 spans) and travelled about 300 million miles while orbiting the Earth.
I probably answered my own question right there but is there anyone you think who could top that?
Not likely.
An airline pilot might conceivably log 40,000 hours in a career. If we assume average speed is 500 mph, that would be 20 million miles - not a large fraction of what’s possible in space.
If we consider a truck driver, the situation is worse: Assume a career of 50 years driving 2000 hours a year at an average of 60 mph - that adds up to just 6 million miles.
The current record is Valeri Polyakov who traveled 300,765,000 km aboard the space station Mir.
http://en.wikipedia.org/wiki/List_of_spaceflight_records#Ten_longest_human_space_flights
I think flight attendents have less restrictions on their flying hours than pilots.
Here is a story about a flight attendent that has racked up 26 million miles. That is over 41 million kilometers and 63,000 hours.
http://www.cbsnews.com/stories/2010/12/28/eveningnews/main7192655.shtml
Extending the definition of ‘travelled’…
By comparing the Doppler shift of the cosmic background radiation in different directions we can determine that we and everyone else in the Milky Way are travelling through space at approximately 1.3 million miles per hour.
The longest living human was Jeanne Calment who lived to 122 years and 164 days. During her lifetime, she must have travelled just short of 1.4 trillion miles.
Who has travelled the most overall distance. 
So, what you’re saying is:
The sun and you and me and all the stars that we can see
Are moving at a million miles a day
In an outer spiral arm, at forty thousand miles an hour,
Of the galaxy we call the ‘Milky Way’.
Yes, that was his question.
That would assume the OP restricted travel only to living people. Someone who’s remains are intact that lived thousands of years ago would have traveled much further than the oldest recorded human lifespan.
Nevermind…:“lifetime” was a precondition.
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The Wiki page you linked to (interesting read, there) also says “Sergei Krikalev has spent 803 days, 9 hours and 39 minutes, or 2.2 years in space over the span of six spaceflights on Soyuz, the Space Shuttle, Mir, and International Space Station.” but doesn’t say how far he’s traveled.
Does it count as travel if you’re just going around in circles?
If it doesn’t , then we can’t count any commuting mileage either for flying or driving. For that matter, I had a friend that went to Indonesia over the Atlantic and came back over the Pacific.
But he was in orbit, right? That’s basically just falling and missing the ground. I think he should be disqualified. I think to be “traveling” you need to be in the process of going towards a destination, it can’t just be “movement relative to the Earth’s surface.” How far around the Earth did the moon move while the astronauts were on it? Does that count?