Can iodide dissolve in organic solvent?

simply, iodine,I2, has weak van der waals' force between iodine molecules
and those organic solvent has weak intermolecular force(van der waals' force)
, so their forces are comparable and so iodine dissolve in organic solvent.

While I- ions(in ionic compound), has strong ionic bonds which is not comparable to weak intermolecular force, so they are immiscible.

To remind you a skill, when attempting this type of question, you should identify their BOND WITH STRUCTURE.

To the poster above me: I won't call 'chloroform' a 'NON-POLAR solvent'!!! It has a polarity index of 4.1! Compare this to hexane, which has a polarity index of 0 - now THAT is NON-POLAR!!! In fact, a lot of organic compounds will dissolve in chloroform (that's how we run NMRs as well, with NMR chloroform!), so you can see how powerful chloroform really is.
Iodide - an ion with a negative charge, is insoluble in organic solvents, simply due to the -ve charge. Rememeber, that anything that carries a charge, either +ve or -ve will be WATER SOLUBLE. To get I- in solution we usually need to have it as an inorganic salt in water for I- to be disassociate.
Iodine is soluble in most organic solvents because it doesn't carry a charge.
Remember:
No charge - organic solvents soluble
Charged - water soluble