I have a simple text area in a form like this:
I got the same problem, and the solution is very simple: don't start a new line! Although some of the previous answers can solve the problem, the idea is not stated clearly. The important understanding is, to get rid of the unintended spaces, never start a new line just after your start tag.
The following way is WRONG and will leave a lot of unwanted spaces before your text content:
The RIGHT WAY to do it is: