Edit: if you can make it work for you, major kudos. Maybe some pointers for us who don't see the advantages?
Autocracy is one of the most powerful polices in the game.
Picking Autocracy slashes unit maintenance by 33%. Late game, this usually means saving ~100 gpt.
The next two policies available are very powerful. Populism gives wounded units a 25% combat bonus. Think about that - in a war, units are always getting wounded. Thus, this 25% bonus will apply nearly all the time. It's almost like having a second, more-powerful great general.
The other policy available is even better - it gives you a 33% discount on units rush-bought at cities. Combine this with the Mercantilism policy, which is two SPs into Commerce (gives a 25% city purchase discount), and now you have units costing less than half the price as normal. Turn your mines and farms into trading posts and you will find yourself affording mech infantries every other turn.
Then, of course, there's fascism, which doubles all strategic resources. This is an invaluable policy. If you're short of oil or aluminum, fascism can be game-breaking. If you're not facing shortages, you can also make big moola, for example, by selling your spare uranium to Hiawatha on the other side of the map. My last game I did this, making about 1000 gold's worth of stuff every 25 turns, and as a bonus, Hiawatha nuked the hell out of my sworn enemy China.
Yes, Autocracy does disable the awesome bonuses from Freedom, and makes you lose out on Meritocracy (as Randall Turner was complaining), but Police State, providing a whopping 50% unhappiness reduction from occupied cities, more than compensates. A large empire can get as much as 10 or 15 happiness points from Police State.
Finally, there's Total War - 20-turn 33% combat strength bonus to all units. This policy frequently gets bashed for not having permanent effects, and I agree: but I also feel that Total War is underrated and extremely powerful in the right hands. The 33% bonus is very significant when launching an invasion. With mech-infs, 20 turns is more than enough to cripple enemy forces and take most of an enemy’s cities while leaving the rest exposed and unprotected. Total War is usually worth the SP, especially because there's not much else to invest your SPs into.
So how exactly does one use Autocracy? Play as France or Greece. I recommend disabling all victories except Domination, though it is not necessary, especially if you are going for cultural. Sink your first 3 SPs into Commerce to get Mercantilism. Sink two more into Freedom to get Constitution. Ignore Free Speech, unless you’re going for cultural. Get a cultural CS, if you can, especially if you are Alex. With a museum and an opera house and wonders etc., I was gaining 100 culture per turn in my capital (I’m not exactly sure how that was happening, but it was.) and getting SPs every ten turns, despite having 7 cities (this was on quick, with no XML tampering). Keep it up until you have about enough for 5 or 6 policies, then make the switch to Autocracy.
Then proceed to wipe the AI off the face of Pangaea.