So. You may have started the game, set up your options and wanted to start playing to find your character slowly moving forward of his own accord.

When strafing he will begin running in this direction making it impossible to strafe properly and can make platforming an annoyance.

Simple.

Options > Controls > Advanced.

Here you will find a deadzone slider...

This slider determines how far the controllers stick needs to be pushed to go from walking to running.

Too much means your character will run constantly.
Too little means he will walk constantly.

You will need to find the correct value for whatever controller you are using. For my Xbox 360 Elite Controller it was here in this picture which is the default setting (Atleast for me).