Jamie Andreas has made an entire industry around the whole relaxation issue - I have her DVDs at home and personally think they are a little over the top, but there's no doubt relaxation is important. For me, tension is a constant enemy.
You hear this advice about letting gravity pull your fingers onto the fretboard - but if my understanding of physics is correct, unless you are laying on your back, that isn't going to happen - so I've never really understood that idea - but would be glad if someone could enlighten me.
I suppose if the fretboard is facing slightly skyward, there's an element of downward pressure there.
One thing I find useful whenever I find the 'death grip' overcoming my fretting hand (which is often - but less often than it used to be) is to
consciously really think hard about what it is I'm trying to do - ie push the string down just behind the fretwire - not push the string down onto the fretboard, and I try to do this with as little effort as possible. I watch the distance between the string and the fretboard too, to re-inforce that. That may or may not help you - in some strange way it helps me quite a bit.
Its funny - somedays I still feel like I have to push harder than others - but again, this is becoming less frequent. Other days its just like a feather-touch.
Well, that's my 2 cents.