I look at the special units in terms of their relative increase over their counterpart and the timing for the golden age when used.
Ideally you would want to enter golden age when you have just completed your 'core' (cities that have acceptable corruption) as you get the greatest relative increase of both the extra shield and the extra trade per square. You may want to wait for some minor improvements to existing terrain if there is not enough shield+trade squares to utilise though. Both of these factors point toward an early/middle age unit.
1. Iroquois Mounted Warrior - Almost perfect Golden age timing, 50% increase on attack stat, fast unit. Although they need horses, you seem to be able to pick them up pretty easy from all the scouting. A tribe of these can rule the whole era until gunpowder
2. Roman Legions - 50% increase in defense. Due to defense they can afford to sit around longer and time the golden age to near perfection. Really needs barracks to help out with winning battles as there is no retreat, and finding iron seems a bit hit and miss. Although the Persian Immortals seem better on paper, these guys seem to outperform them on the battlefield. Solid, solid unit.
3. Aztec Jaguar warrior - %100 movement increase, and, more importantly, making a normal unit into a fast, retreatable unit. A little too early to fully time a golden age, and originally the reason I poo-pooed them. Once you've played with them they demonstrate how awesome the movement increase is. You can totally ignore other defensive units with these guys in play as you can easily get a 'wave' of souts-come-defenders milling around the outskirts of your civ. Pick up some training on local barbarians before strolling over any closeby civs. Probably THE quickest civ to get a leader -> forbidden palace in place too.