when i ride my bike no handed it pulls hard to the left, so much so that to ride straight my left shoulder has to be practically over the saddle

is that a problem in the head set?
any ideas?

or your frame/wheels are missaligned, or you have really weird body weight distribution

very unlikely to be the headset. sounds like bent frame or wheels

take your forks off and have them aligned.

I used to have this problem no matter what bike I was on. Looking at old saddles I had replaced I realised that I sat really heavy on the side of my saddle. I wonder if it has something to do with differences in leg length? Anyways...It doesn't seem to be a problem any more, though every once in a while I do tend to drift left.

One way you could check I guess is to hop on another bike for a moment and see if you still drift left. If not...then its probably your bikes alignment.

Does that sound like solid advice?

Take the wallet out of your back pocket and try again. Worked for me.

i only wish my wallet was full enough to make a difference

I have a bmx that I got for cheap and the top of the fork is bent. It totally leans to the left when riding sans hands.

if the dish of your front or rear wheel is off, or if your frame is bent, or if you fork is bent it will affect the tracking.

anything i forgot? oh ya, your wallet...

Your left testicle and breast is larger than your right.

is your bag strap on your left shoulder?

but it could be your headset ... my bike was doing this and i loosened my headset a tiny bit as per the advice of someone on this board and that solved the problem. i'm not saying this is YOUR problem but it is worth checking first because the other fixes are complicated.