I was actually asked this myself a few weeks ago, whereas I know exactly how to do this with a SP or UDF but I was wondering if there was a quick and easy way of doing this without these methods. I'm assuming that there is and I just can't find it.
A point I need to make is that although we know what characters are allowed (a-z, A-Z, 0-9) we don't want to specify what is not allowed (#@!$ etc...). Also, we want to pull the rows which have the illegal characters so that it can be listed to the user to fix (as we have no control over the input process we can't do anything at that point).
I have looked through SO and Google previously, but was unable to find anything that did what I wanted. I have seen many examples which can tell you if it contains alphanumeric characters, or doesn't, but something that is able to pull out an apostrophe in a sentence I have not found in query form.
Please note also that values can be null or '' (empty) in this varchar column.
Won't this do it?
SELECT * FROM TABLE
WHERE COLUMN_NAME LIKE '%[^a-zA-Z0-9]%'
Setup
use tempdb
create table mytable ( mycol varchar(40) NULL)
insert into mytable VALUES ('abcd')
insert into mytable VALUES ('ABCD')
insert into mytable VALUES ('1234')
insert into mytable VALUES ('efg%^&hji')
insert into mytable VALUES (NULL)
insert into mytable VALUES ('')
insert into mytable VALUES ('apostrophe '' in a sentence')
SELECT * FROM mytable
WHERE mycol LIKE '%[^a-zA-Z0-9]%'
drop table mytable
Results
mycol
----------------------------------------
efg%^&hji
apostrophe ' in a sentence