If a player casts polymorph and they get more arms, can they have extra attacks with those extra arms?
If they do get extra attacks, what is your base attack bonus?
Is the same true for wildshape? This ability is no longer based on polymorph.
In some cases, yes.
Your Base Attack Bonus doesn't change, whether you use alter self, polymorph or the druid's wild shape class ability (which, as of the 2006 Player's Handbook v.3.5 Errata, functions like the alternate form special ability).
I interpret the above quote to apply only to attacks with manufactured weapons (swords, bows, spears, and the like). For example, if you polymorphed into a creature with four arms then you would still be limited to wielding two weapons at most.
However, you acquire the physical qualities of the new form, which include any natural weapons the creature possesses. You also gain its racial bonus feats, which means that you are proficient with these weapons. The number of attacks that a creature can make with its natural weapons, such as claw/claw/bite, is not dependent on Base Attack Bonus. Therefore, if you change shape into such a creature, you can use the same attack pattern. The penalties for two-weapon fighting do not apply to natural weapons.
For example, if your BAB is +6/+1 with Strength 13 and you alter self into a lizardfolk, then you have the following options for a full attack:
If you polymorph into a giant octopus (with Strength 20) then your full attack would be:
For a total of nine attacks per round.
The Rules of the Game column by Skip Williams has a series of articles on these spells, which I have found very useful:
For polymorph the answer is no, for wildshape yes.
The polymorph spell is based on the alter self spell. The alter self spell specifically states :
My interpretation is that the number of attacks you can have is equivalent to the number of attacks you get when in your normal form. Of course, your new form may have some extra natural abilities that improve your attack, such as rend, constrict etc. If you allow more attacks, you could find yourself in a situation where you have a rogue/assassin that can perform lots of sneak attacks in a single round.
The new BAB will be based on your class and your new STR and DEX bonuses.
The wildshape is not based on polymorph (in the errata), instead it is based based on alternate form. The alternate form does not have the restriction about allowing attacks from any extra limbs. The wildshape ability only lets you change into an animal, where natural attacks are available to you.
This article from the wizards site explains the horrible problem they got themselves into with this entire polymorph ability.