Why would someone use WHERE 1=1 AND <conditions> in a SQL clause?

Just adding a example code to Greg's answer:

dim sqlstmt as new StringBuilder
sqlstmt.add("SELECT * FROM Products")
sqlstmt.add(" WHERE 1=1") 

''// From now on you don't have to worry if you must 
''// append AND or WHERE because you know the WHERE is there
If ProductCategoryID <> 0 then
  sqlstmt.AppendFormat(" AND ProductCategoryID = {0}", trim(ProductCategoryID))
end if
If MinimunPrice > 0 then
  sqlstmt.AppendFormat(" AND Price >= {0}", trim(MinimunPrice))
end if

Seems like a lazy way to always know that your WHERE clause is already defined and allow you to keep adding conditions without having to check if it is the first one.

I've seen it used when the number of conditions can be variable.

You can concatenate conditions using an " AND " string. Then, instead of counting the number of conditions you're passing in, you place a "WHERE 1=1" at the end of your stock SQL statement and throw on the concatenated conditions.

Basically, it saves you having to do a test for conditions and then add a "WHERE" string before them.

If the list of conditions is not known at compile time and is instead built at run time, you don't have to worry about whether you have one or more than one condition. You can generate them all like:

and <condition>

and concatenate them all together. With the 1=1 at the start, the initial and has something to associate with.

I've never seen this used for any kind of injection protection, as you say it doesn't seem like it would help much. I have seen it used as an implementation convenience. The SQL query engine will end up ignoring the 1=1 so it should have no performance impact.