From Diablo Wiki
The Alkaizer run is a popular farming run in Act Three. The run was popularized by the player who was the first to reach paragon level 100 with a Barbarian named Alkaizer. This run was what he did in game after game, thousands of times on his grind to reach the max level. He did it because it was very efficient, with huge numbers of monsters and lots of boss packs along the way, and this run is widely-considered the most efficient and profitable run found anywhere in Diablo III.
On the classic Alkaizer Run, a sufficiently-powerful character will clear (most of) five different areas throughout Act Three, racking up huge experience and killing numerous boss packs very rapidly. The run is best done quickly, on a level of Monster Power low enough that your character can blast through with very little slow down.
 The Alkaizer Run
Though many players have slight variations on the run, the classic run proceeds as follows. The order does not really matter, but this sequence proceeds upwards from the lowest waypoint on the list. Players aim to complete the run in under 15 minutes, with very fast characters able to do it in 10 minutes or less.
- Start game on Act Three, on the last quest: Heart of Sin : Kill Azmodan
- Appear at the end of the The Core of Arreat, clear level.
- Waypoint to Tower of the Damned Level 1, clear level in a circle returning to the waypoint.
- Waypoint to Arreat Crater Level 2, clear level, portal back to town.
- Waypoint to The Bridge of Korsikk. Clear the Fields of Slaughter level in a circle, returning to the waypoint.
- Waypoint to The Keep Depths Level 1, take stairs to The Keep Depths Level 2, clear level and exit game.
- Create new game, repeat.
- Arreat Crater Level 1 is not a lot different than Level 2, though it's not as large an area and often has a long, dead end layout.
- The Keep Depths Level 3 can be easily added on, though it generally has a lower concentration of monsters.
- Some players do The Core of Arreat last, (or at least not first) and then proceed down to kill Azmodan to get his drop with five stacks.
How fast each area is done and how much loot is picked up varies between players, but the whole point is to clear the areas quickly and efficiently, so it's recommended that players move through rapidly and only pick up a few potentially great items, rather than grabbing all the gold, tomes, gems, etc.
- Consult the Unidentified items key for a handy list of all ilvl 61-63 item types and memorize the names of the ones you're after, so you don't waste time picking up item types you're not after.
The value of these levels, especially the Tower of the Damned 2 and the Fields of Slaughter, is that a player can move around the entire area very quickly, getting all boss packs and most of the regular monsters without detours or slow exploration. This is less true of the Keep Depths Level 2, and some players skip that area, or don't bother to detour back to any cul-de-sacs they missed there, or in the large Arreat Crater Level 2.
 For Experience
When Alkaizer was rushing for Paragon 100, he picked up nothing but Legendary items, Set items, and rare Slayers (the ilvl 63 one-handed Mighty Weapon sword). His priority was entirely the experience gain, with a much lower importance placed on item finds.
As of Patch 1.0.6 it's most efficient to play on MP0 for the fastest possible killing, since the additional experience from higher levels of Monster Power does not pay off. This equation may change in Patch 1.0.7 with the planned increased experience awards from higher levels of MP.
Players who wish to emulate this style might pick up more gear, but the key is to grab during the action and keep moving. Most players leave behind countless items and stacks of gold and only kill most of the enemies; the ones that come into easy range. It's counterproductive to linger over items, or to chase down every last monster. Just kill the bulk of them, grab the very best potential items, and hurry along.
This run is a very good way to score huge experience since there are vast numbers of small, easily-killed enemies along the way. That's where the biggest experience gain comes from in Diablo III on Inferno difficulty. Bosses have a small bonus to their experience value, but they take longer to kill than normal monsters and thus are not the best source of experience.
The key to earning the maximum experience is to kill as quickly as possible and to keep moving on, hitting numerous enemies with every attack. The popular and overpowered Spin2Win Barbarian build works very well for exp rushing, since most of the damage is done by tornadoes left behind by Sprint: Run Like the Wind and/or Whirlwind: Dust Devils, which continue their DoT killing while the Barbarian himself is far away.
 For Items
Playing the Alkaizer Run for items still nets you experience and players shouldn't entirely abandon the concept of rushing, but players who are more interested in finding good gear will want to do this run with as much Magic Find as possible, while still maintaining a rapid killing speed.
Picking up everything is counter productive, since the time spent gathering gear and (especially) identifying it and taking it back to town to sell is inefficient. The gold earned from that, and the likelihood of a rare item actually rolling top quality mods is so low that players can make more profit simply grabbing the good stuff and the gold on the ground while continuing to kill as quickly as possible.
Players who want to gain loot from Alkaizer runs should memorize the names of the top rare items to know what they want to pick up quickly. In addition to the Legendary and Set items, many players pick up only ilvl 61 and above Rares, or only Rare jewelry, or only Rare one-handed weapons, depending on their needs or what they think is most likely to pop with good mods.
- List of all ilvl 61-63 item types.
Videos of some successful runs can be seen below:
A Monk with 200DPS has a successful run.
Barbarian WW/Sprint build, with narration.
Wizard with Archon in a very fast 10 minute run.