MOST of the time, I'd say that a GPS is the most important thing to have on a chase FOR ME. It's helped to easily navigate many backroads, and comes in particularly handy during fast-moving-storms days or days in which you chase in areas with complex (non-gridded, etc) or sketchy roads. Other days, however, it's been my ham radio that has saved the chase (spotter nets, weather radio, etc).
Camera and camcorder are important, but I'd still chase even if I didn't have either of those... I chase because I love the feeling of it and love witnessing the raw power, so being able to document it, while nice, isn't an absolute necessity. After all, I have my memory...
Data access is nice, but again, not a necessity IMO. Ppl were chasing long before widespread cell data or WxWorx and seemed to score just fine... Yes, data is very nice to have while on the road, but not a necessity.
Ah yes, and for those times you begin to hydroplane, or realize that your staring down a 8"-deep mud road, good tires are quite comforting!