Can a person or spacecraft land on a gas giant, like Jupiter?

Yes, there's a Critical point where gas gets squeezed into a liquidish gas. After this you fall a little then get to the point where you are less dense than the liquid, meaning you will float there. read more

So, you couldn't exactly stand on this ocean. But below this, it's thought Jupiter may indeed have a rocky core, perhaps somewhat similar to terrestrial planets. Juno will help answer this question during its mission. Jupiter has most of the planetary mass of the Solar System, and could easily fit all the other planets in its interior. read more