D&D Question: Multiclassing and BAB
 

So, for example, say Im a 3rd level fighter. I have a Base Attack Bonus of +3. I decide to take a Ranger level, and 1st level Rangers have a BAB of +1. What exactly is my BAB now?

I'm having the weirdest deja vu. I think you asked that before at some point, didn't you?

Anyway, your BAB is now +4. +3 from the Fighter levels, +1 from the Ranger levels. You always add up the BAB values the tables for each single class give you. You calculate iterative attacks from your highest BAB, though, so if you took two more levels of Ranger now, your BAB would be +6/+1. Saves work the same, just in case.

Probably. I tend to forget things. So basically just add it for the level of whatever calss I just took?

Just add them up it's really simple.

If you're Fighter 3/Sorceror 1/Rogue 1 you'd end up having a BAB of +3

A Fighter 3/Barbarian 2/Ranger 1/Paladin 2/Rogue 2 would have a BAB of +9 (1 for each level of the full BAB classes and a total of +1 coming from the Rogue classes)

Can you even have 5 classes?

You could theoretically have 1 level in 20 different classes.
(This is ignoring epic levels.)

In fact, I bet that would be fun as hell to play. Not very effective, but fun as hell.

Technically (and if you were using some rules out of Unearthed Arcana), this would add up to +4, being +3 from fighter, +.5 from Sorceror, and +.66(Repeating) from Rogue, giving you a BAB of +4.16

As this requires math however, the corebooks don't track fractional progressions of saves or attack boni from multiclassing, because it'd get hella confusing this way.

(Argh, gestalt rules! argh!)

Fiddly math aside however, I think it's fairer to any (non twinking) person who takes more than 2 classes that aren't PRCs, as they're going to be incredibly gimped anyway, possibly even attaining a BaB worse than a pure wizard, which shouldn't even be possible. On the other hand, Ness, you're not entirely correct. Taking 20 level 1 classes doesn't give you any xp penalty, and you get the level 1 saves from every class.

Your BaB will suck, but your saves will exceed God's.

I used to ask the same thing, due to games like Neverwinter Nights which limited your D&D progression to a maximum of 3 classes. But there is no such restriction in actual D&D.

Other than the painful experience penalties that will apply if favored class is anything but "Any".

Those only apply for... *grabs his PHB* ... More then 1 level apart from each other.