Rules for succesfully capturing various aliens in XCOM

None need special conditions. The less health they have the more likely you are to succeed. No conditions result in a 100% capture chance as far as I can tell (the highest I've seen is 95%, with the enemy at 1 health and the advanced arc thrower researched at the Foundry). The unzappable ones are Chryssalids, Drones, Cyberdisks and Sectopods, as well as the Mechtoid and Seeker from Enemy Within. Another upgrade at the Foundry will give you the ability to use the Arc Thrower to "reprogram" drones to fight for you, but they will explode at the end of the mission, you will not be able to interrogate a drone no matter what you do.

I find attacks that deal a set amount of damage (grenades, rockets, first psionic ability) and low-yield attacks (pistols) to be great for capturing, as you can bring a target's health down in a controlled manner without risking its death to maximize chances of a successful capture.