I would not fill them, They will collect other debris and look awful in short order.

Ah never thought of debris getting stuck, good point. So you think we should just deal with the gaps? We can put rugs down for some of it, I suppose..

The gaps are there for a reason. They help prevent water from pooling on the surface and allow air flow to dry out the boards evenly on all sides. They also give the boards room to swell and shrink in response to changing humidity. While 1/2" gaps do seem excessive to me, boards without enough gap spacing are far more likely to cup and buckle as a result of changing moisture levels.

I'd pull them up a section at a time, butt 'em tight and renail. Those boards are as cupped as they're ever going to be and you're never going to be able to butt them tight enough to prevent water evacuation.

You can also use a board stretcher, if not replace the decking.