In terms of pure market share percentage, UBS and Macquarie are the largest equity trading houses. Macquarie have a strong derivatives division, and UBS have a strong fixed-income division.
UBS has the largest trading floor in the southern hemisphere (I think that is what they said). If you ever get the chance to go down there, the place is incredible. You get pumped from just walking in the door.
Check out the Thomson league tables for debt and equity:
Here
Here is the most recent overview:
Here
Its pretty much UBS, Macquarie, and JP Morgan.