I'm going to go against popular belief and say not to move it. Most of the time, as others have pointed out, they do just fine. But some cats won't do fine, and that's when they start peeing all over the house. This can be a major headache to break them of once it's happened. Sorry, I've just seen too many cats given up b/c of this very issue.
The behavior experts recommend the following:
One box per cat, plus one extra
No hoods
No perfumed or scented litters
Keep boxes in an EASILY ACCESSIBLE, quiet area - this rules out downstairs in the basement next to the furnace/washing machine/dryer
Spread multiple boxes throughout the house, not all lined up next to each other. Have at least one box on every level the cat has access to.
Scoop boxes at least once a day - once a week is not good enough - would you go in a used toilet? Your cat doesn't want to either.
Change out all the litter once a month
Replace the entire box once a year, as the plastic will absorb odor over time
Most people don't follow half of these, and their cats do "fine," but when the cat suddenly stops using the box, they can't understand why. If you take these steps, you can avoid potential problems in the future.
Also consider this: hopefully your cat will live to a nice old age. If he does, he's likely to develop arthrithis. Those basement stairs will be a major obstacle at that point and he might just go find a more convenient spot on his own.