Not many.
Since Resilient Sphere is essentially a spherical wall of force, and wall of force breaks line of effect, you cannot cast through it. Any spells targeting an enemy through the sphere fizzle.
Summon monster should not be able to summon anything outside of the sphere. The caster needs line of effect to the point where the monster will be summoned, and resilient sphere prevents this.1
Psionics, if they count as spells, also cannot pass through, unless they specifically ignore line of effect (I don't have the occult book so I don't know much about Pathfinder psionics).
Hexes are a gray area. There is very little information on how they interact with magic, other than them being supernatural abilities. Since they should still follow the general magic rules, I believe they must also have line of effect.
Gaze attacks are specifically called out as working through wall of force, but I don't know of a way to gain a gaze attack off the top of my head. There are no spells that qualify as gaze attacks, either, as far as I know.
1 This is debatable, but probably how I would rule it. The question is, is this spell similar at all to teleport or dimension door? It could be considered either. On one hand, you are designating a location, just like Dimension Door. On the other hand, the range is much shorter. The major difference is, Dimension Door targets you, and you are already inside the sphere.
Yes, you can enter the circle
The resilient sphere effectively excludes anything it encloses from outside spell effect areas. As the effect of the magic circle originates outside, it does not have any effect on a creature rolling inside the sphere, as it is not considered to be in its area of effect.
Best Answer
Otiluke's Resilient Sphere blocks the ghost's ethereal travel
Any wall of magical force exists in and blocks movement in both the plane it exists on and the corresponding border ethereal, as described in the DMG's section on the Border Ethereal (emphasis added):
Otiluke's Resilient Sphere, which is a magic spell, creates "a sphere of shimmering force", which means the sphere's barrier is made of magical force that blocks ethereal travel. Hence, even if the ghost goes into the Ethereal Plane, it is still unable to enter the sphere (or escape it, if is trapped inside).
Incorporeal Movement probably doesn't help the ghost either
In addition to having access to the Ethereal Plane, the ghost also has Incorporeal Movement, which simply lets it pass through most things regardless of what plane it is currently on:
Unfortunately for the ghost, I don't believe a creation of magical force is the same as an object. I don't have an explicit reference for this, but for example, the text of disintegrate lists "object" and "magical force" separately, as if they are considered different things:
Hence, I don't believe that the ghost's Incorporeal Movement is intended to allow the ghost to pass through barriers of magical force.