My grip strength is great, and I contribute it to never using gloves, and rarely using straps. Some argue that I am not getting a good back workout in by not using straps, but IMO, compound exercises are designed to help you work a multiple things and that our bodies work as a system. I want as few weak links as possible.
That said, I will admit to using straps on my heaviest set of pulldowns. Reason why, is that the bar is smooth, and even with a great grip, you just can't hang on to it.
I also do BB shrugs, and when my traps are fatigued, I hang on to the bar until my grip gives out.