How do I solder headers so that they always stand straight up?
If these are boards that you are designing, then is there something you can do to make it easier to solder header on straight. If you stagger the holes like this:



(image and concept from SparkFun) 

...then the header will essentially lock into place when you insert it. Doing it this way, you probably won't even need any special soldering techniques.

If you're using Eagle, SparkFun's library has many pin header footprints that "lock" like shown.