Not Updated For Current Season
This is just a silly Sion build I've used in some games. I've seen similar AS builds before, but none as dramatic.
Get a Sapphire Crystal. Stun and swing at everything. Last hit as much as possible. Focus on your Enrage.
You should be attacking Scary-fast already, and with your innate life leech/AS buff, should be hitting uber-quickly, really hard, and healing yourself when you get low. Use your shell(Death's Caress) to absorb the damage cost from Enrage, not to deal damage itself. Stun and swing everyone. You should be able to obliterate a tower with just a single tank-minion horde.
By this time, you should be reaching 2.0 attack speed, 2.5 when you pop Cannibalism. You should be dealing roughly 170dmg per swing, not including Malady or Divine's proc. You should be able to pop a stun every 5 or so seconds. You should be able to out-leech most everyone's damage, so long as you're not disabled. You should be fast, crit regularly, and shred your foes.
This item set is absolute.
You need the two cooldown reduction talents for this to work. This build assumes you'll never actually get the Nashor's or the Frozen Heart, because you'll dominate the game so fast. If you find all of your games running long, or you get rich as hell, you can swap talents over to full-offense.
I can see swapping in cleanse or exhaust, but honestly, popping ignite after stunning and shredding someone, or chasing them down so you can stun and shred people seems evidently more useful.
Addendum: This is a silly build. I've only played it a few times with mixed results. It does, however, wreck like a steam-roller if you can pull it off.