Which of the following is most stable?

Apply Huckel's rule for aromaticity.

A cyclic, planar, fully conjugated system is aromatic if it has $$(4n + 2)$$ $$\pi$$-electrons (where $$n = 0, 1, 2, ...$$), and antiaromatic if it has $$4n$$ $$\pi$$-electrons. Aromatic species are exceptionally stable, while antiaromatic species are very unstable.

Analyze each species.

Option A - Cyclopropenyl cation ($$C_3H_3^+$$):

This has 3 carbon atoms in a ring with one positive charge. Number of $$\pi$$-electrons = 2 (one double bond contributes 2 electrons; the cationic carbon has an empty p-orbital). With $$4n + 2 = 2$$ ($$n = 0$$), this is aromatic and highly stable.

Option B - Cyclopropenyl anion ($$C_3H_3^-$$):

This has 4 $$\pi$$-electrons. With $$4n = 4$$ ($$n = 1$$), this is antiaromatic and very unstable.

Option C - Cyclopentadienyl cation ($$C_5H_5^+$$):

This has 4 $$\pi$$-electrons. With $$4n = 4$$ ($$n = 1$$), this is antiaromatic and unstable.

Option D - Cyclohexadienyl:

The cyclohexadienyl species is not fully conjugated (it has an $$sp^3$$ carbon breaking the conjugation), so it is non-aromatic and less stable than an aromatic species.

Conclusion.

The cyclopropenyl cation (Option A) is the only aromatic species among the choices, making it the most stable.

The answer is $$\boxed{\text{Option A}}$$.