Step 1: Free energy change (\(\Delta G\)) in reactions.
- Negative \(\Delta G\) indicates that the reaction is spontaneous and can proceed without external energy input.
- Spontaneous reaction: The reaction will proceed in the direction where the free energy decreases.
- Exergonic reactions: These are reactions that release energy, corresponding to a negative \(\Delta G\).
- Option (B) is incorrect because negative \(\Delta G\) indicates the free energy of the products is lower than the reactants, not higher.
- Option (C): While high activation energy can exist in some spontaneous reactions, it is not required for a negative \(\Delta G\).
Step 2: Conclusion.
Thus, the correct options are spontaneous reaction and exergonic reactions.
Final Answer:
\[
\boxed{\text{(A) and (D) only}}
\]