David's code is great, but I don't understand it at all. I typed up my own code in two versions. First I made a random finder that found 81, then I devised a systematic way to get all of the answers. Here's the kicker:

The program only yielded 188 answers.
I ran through and compared equations, and realized that I had fallen to the almighty "roundoff error". I fixed the bug, but the code still only gave me 190, not 191. Either I was missing one or David had an extra.

I reformatted my code to output in the same order as his, and I found out that David's 189th equation wasn't on my list. Sorry Dave, but

1 / 2 / 3 + 4 - 5 * 6 + 7 + 8 - 9 = -1, not 1

anyway, so there are only 190 solutions, not 191. Here's my program if you want a peak, I made it as friendly as possible. Notice the loading bar. Non-friendly version: 52 lines long.

DEFINT A-Z 'setup of program
OPEN "c:/solution1.txt" FOR OUTPUT AS #1 'open file for output
CLS
LOCATE 3, 1: PRINT STRING$(62, ".") 'print empty loading bar
start$ = "1 2 3 4 5 6 7 8 9" 'set equation template
DIM j$(5)
j$(1) = "+" 'these are the five possiblities
j$(2) = "-" 'for between numbers" nothing,
j$(3) = "." 'and the 4 operators.
j$(4) = "*"
j$(5) = "/"

'test every possibility
FOR s = 1 TO 5: FOR t = 1 TO 5: FOR u = 1 TO 5: FOR v = 1 TO 5
FOR w = 1 TO 5: FOR x = 1 TO 5: FOR y = 1 TO 5: FOR z = 1 TO 5

IF s = 3 AND t = 3 THEN GOTO nexttest 'no three digit numbers
IF t = 3 AND u = 3 THEN GOTO nexttest
IF u = 3 AND v = 3 THEN GOTO nexttest
IF v = 3 AND w = 3 THEN GOTO nexttest
IF w = 3 AND x = 3 THEN GOTO nexttest
IF x = 3 AND y = 3 THEN GOTO nexttest
IF y = 3 AND z = 3 THEN GOTO nexttest

FOR q = 1 TO 5: IF q = 3 THEN q = q + 1
IF s <> q AND t <> q AND u <> q AND v <> q THEN 'must include all four
IF w <> q AND x <> q AND y <> q AND z <> q THEN 'operators:+-*/
GOTO nexttest
END IF
END IF
NEXT q
'ok, the equation is
'valid. Build it.
'put all the operators together
a$ = j$(s) + j$(t) + j$(u) + j$(v) + j$(w) + j$(x) + j$(y) + j$(z)

'put the numbers and operators together
dat$ = start$
FOR q = 1 TO 8: MID$(dat$, q * 2, 1) = MID$(a$, q, 1): NEXT q

'get rid of the dots.
a$ = ""
FOR q = 1 TO 17
IF MID$(dat$, q, 1) <> "." THEN a$ = a$ + MID$(dat$, q, 1)
NEXT q
dat$ = a$

'solve it

solve! = VAL(dat$)
FOR r = 1 TO LEN(a$) - 9
dat$ = MID$(dat$, LEN(STR$(VAL(dat$)))) 'next number
b = VAL(MID$(dat$, 2))
SELECT CASE MID$(dat$, 1, 1) 'look at sign
CASE "+": solve! = solve! + b
CASE "-": solve! = solve! - b
CASE "/": solve! = solve! / b
CASE "*": solve! = solve! * b
END SELECT
dat$ = MID$(dat$, 2) 'next sign
NEXT r
solve! = INT(solve! * 10000) / 10000 'fix comp error

nexttest:
key$ = INKEY$: IF key$ <> "" THEN END 'check for exit
NEXT z: NEXT y: NEXT x: NEXT w 'next
lb! = lb! + .1 'update loadbar
LOCATE 3, 1
PRINT STRING$(INT(lb!), "_*")
NEXT v: NEXT u: NEXT t: NEXT s 'next