Ignoring all erratas you can get....408 attacks in a single round (At ECL 40ish, though)
Here's how:
Assuming 4 attacks with BAB of
Start with, Nezumi (ratmen) from Oriental Adventures, with Exotic Weapon Proficiency (Tail Ring) or whatever that's called, it basically gives them an extra attack, at a penalty of -2 to all attacks for that round.
Toss in that Maho template, giving them 6 extra arms.
Manifest psionic power like Bite of the Wolf to grant an extra bite attack
Add in Multidexterity, Improved Multidexterity, and Superior Multidextery for a total of 4 attacks with each appendage (8 arms, 1 tail, 1 bite)
Starting total: 40 attacks
Lightning Fists, from Sword and Fist, by it's direct wording does not need to be used in conjunction with unarmed attacks, so you can gain 2 extra attacks at your highest attack bonus when taking an FRA (penalty to other attacks), net +2 attacks
Make all the weapons for the 8 arms and tail speed, it stacks with itself but not haste by 3e DMG wording (not sure on future editions), net +9 attacks.
Gain enough levels in Thrall to Demogorgon (2 or 4?) from the Book of Vile Darkness to gain, 2/day, an extra full attack in the round. Double all attacks for a total of 102 attacks.
Get an item with Battletide (Magic of Faerun) which grants an extra partial action per round (but stacks with and is not considered Haste by it's wording), combine this with Warrior of Darkness from BoVD and gain Black Magic Elixer, choosing the Malign Fury option, which allows you to 3/day gain a full round action after a move or standard action. Use Battletide's action to move and execute an additional full round attack. Total of 204 attacks so far.
Get 10 levels of Whirling Dervish so you can double all the attacks you make on a full round attack. Total of 408 attacks.