Found this while digging for an answer:
SELECT REPLACE(
REPLACE(
REPLACE(
LTRIM(RTRIM('1 2 3 4 5 6'))
,' ',' '+CHAR(7))
,CHAR(7)+' ','')
,CHAR(7),'') AS CleanString
where charindex(' ', '1 2 3 4 5 6') > 0
The full answer (with explanation) was pulled from: http://techtipsbysatish.blogspot.com/2010/08/sql-server-replace-multiple-spaces-with.html
On second look, seems to be just a slightly different version of the selected answer.