I've been using this for some time:
SUBSTRING(str_col, PATINDEX('%[^0]%', str_col), LEN(str_col))
However recently, I've found a problem with columns with all "0" characters like '00000000' because it never finds a non-"0" character to match.
An alternative technique I've seen is to use TRIM:
REPLACE(LTRIM(REPLACE(str_col, '0', ' ')), ' ', '0')
This has a problem if there are embedded spaces because they will be turned into "0"s when the spaces are turned back into "0"s.
I'm trying to avoid a scalar UDF. I've found a lot of performance problems with UDFs in SQL Server 2005.