The last Internet site listed also has links to accessibility information in other European countries.
The Vatican and St. Peter's are ramp equipped and there is plenty of help available for getting over the hard parts -- a few stairs and thresholds. But the lower church is only accessible by a narrow stairway and the basilica Dome is impossible for all but the most mobile and fit. The Vatican museums do have elevators, and, if you show up with a wheelchair, you will be directed to them.
Romans are extraordinarily kind to less mobile tourists and will make way in lines and offer to help.