Since the underlying conflict is Shia (well, Alawite) vs Sunni, predictably, almost all[1][2] surrounding countries support the combatants they belong with:
- Hezbollah-led Lebanon and Iran support Al-Assad
- Sunni-majority countries (Turkey, Saudi Arabia, Quatar, even Hamas-controlled Gaza, etc...) support the anti-Assad forces. Obviously, the degree and explicitness of support varies between Turkey/KSA, and Jordan.
- Iraq was split, predictably, with ISIS and other Sunni based forces fighting against Al-Assad and Hezbollah whereas Shia forces fighting for Al-Assad (e.g. al-Abbas brigade).
[1] - As you can guess, the only 100% deviation from this rule is Israel. The strategy there is: let them fight each other, helping either side is a losing proposition. The longer they fight and weaken each other, the less they try to harm Israel. So they clearly have no interest in "help prevent the conflict" part of your question. The only times they intervened was when Al-Assad was transfering advanced weapons to Hezbolla, which would be used against Israel.
[2] - Another deviation is Egypt. While it had some support for the rebels during Morsi government, Al-Sisi's main concern is regional stability; preventing Moslem-Brotherhood-sympathetic Sunni refugee inflow; and financial support from regional backers (KSA) who are instead now more concentrated on Syria.