>In a form, I have the formula to check a field X of a table --- if X = "" ...
>It works fine when I run the form in VFP. But it has wrong operant error after I complie it to an exe file.
>Finally I change it to if empty(X) ... then it works fine in both VFP and in its exe file. Does it mean we should use the empty() instead of = "" if we want to check empty field?

See the command SET EXACT.
Depending on SET EXACT the results they are different.

Example:

lc = "    "
SET EXACT OFF
? "" = lc
  >>> .F.
? EMPTY(lc)
  >>> .T.
SET EXACT ON
? "" = lc
  >>> .T.
? EMPTY(lc)
  >>> .T.

I advise to you to use EMPTY()