I believe that the operator is !=
I use field = for a blank field
I use field =* for nonblank field (aka has any content)
"I know there is an omit function, but I do finds with several criteria that include both equal to and not equal to."
If the find contains several criteria, you could add new requests.
Home > Using FileMaker Pro > Finding, sorting, and replacing data > Finding records > Finding records except those matching criteria
To expand on Raybaudi's answer
Let's say you want to find all records where Field 1 = "Apple" but not when FIeld 2 = "red" or "blue"
The following example can be done manually or in a script:
Enter find mode
Specify ==Apple in field 1
Create a new request (Select from records menu or use New Record/Request)
Specify ==Red in Field 2
Select the Omit option (click the button or use Omit Records Script step)
Specify ==blue in field 2
Select the Omit option
Perform the find
The key rule is to make the "omit" requests the last requests in the requests that you set up for your Find.
See this thread for some examples of scripted finds: Scripted Find Examples