You start with 12 spaces. There are 10 claptraps that will give you a backpack SDU. Each backpack SDU gives you 3 spaces.
However, that's just playthrough 1. In Playthrough 2, the claptraps have a CHANCE of giving you another backpack SDU. I can confirm that simply missing that claptrap on playthrough 1 will NOT always yield a backpack SDU on playthrough 2. The chance that a claptrap will give you a backpack SDU on playthrough 2 is quite slim.
So the max amount of spaces you can have (going through both playthroughs) is 42-72. Most of the time, you'll end up with 42-48.
--- If your parents never had any children, chances are you won't have any either
Joining an online game can bug up stuff, possibly if the other players have edited ini's and whatnot, I'm not sure. I played my Siren alone up to level 32, joined a match and the next time I played alone noticed I could hold 83.