How many....

[NDblue]

ASA only here (statewide) for FP and SP except the college level where I think they use NCAA. We don't have LL softball and they just started a 12U league this past summer. I've heard rumors that they might start HS ball next year as a club sport to begin with in this part of the state but nothing concrete yet.

[SC Ump]

NFHS for high school and NCAA for college.

In order of popularity (by my unofficial estimation), the recreational leagues and tournaments include:
NSA*, ASA*, USSSA*, ISA*, Dixie Youth, Little League.

*Asterisk are those profiteering organizations (by my unofficial opinion) that require you buy shirts from them.

[Dakota]

3 for me... ASA, NFHS, and AFA.

[tcblue13]

2
NSA, NFHS
We have ASA and NCAA in the area but I don't do them

[JEL]

ASA, (with and without GRPA addendums) NFHS, NCAA, for softball.
NFHS, NCAA, USSSA, DIXIE (with local addendums) for baseball.

It can get confusing!

[shipwreck]

We have ASA for summer ball.
NFHS for High School ball played in the Fall.
NCAA used in Fall for college ball and regular season in Spring.