You could try this:
select *
from yourtable
where ltrim(rtrim(yourcolumn)) = ''
The idea is that if trimming the value leaves you with an empty string, then all you had in the first place was whitespace.
You could also just do this:
select *
from yourtable
where yourcolumn like ' '
Note that I have tested the second query on SQL Server 2008 R2, and it doesn't work on 2014 as stated in the comments by @gunr2171
Finally, if you have tab, carriage return or line feed, the above will not work. What you can do is to first replace these values with a blank string, and then use the first query like so:
select *
from yourtable
where ltrim(rtrim(replace(replace(replace(yourcolumn,char(9),''),char(10),''),char(13),''))) = ''
char(9)
,char(10)
and char(13)
are used for tab, line feed and carriage return respectively.