Yeah, no problem. Basically, the criteria parameter in SUMIF has to a be a string. So, given the specific example you give, you'd put in
=SUMIF(B1:B5,"<>9",A1:A5)
As in, find everything that's not equal to 9. Off course the problem with that is the value 9 will change with a different column of figures.
So, to get around that you need to replace 9 with the Maximum value in the column, hence MAX(B1:B5). That gives you a number back. Since the criteria has to be a string, you need to convert that number to a string using the TEXT function. Then you just add "<>" and the string together using & to create one big string. At that stage, you have a string in the criteria field.
Hope that makes sense!