I've been pondering your question while working in the shop for that last couple of days. For me, the most important call I can make is one that is as realistic as possible. I think cadence is just as critical as sound, whether I'm trying to sound like a hen, jake or gobbler. Like Bill I like a raspy old hen sound for a couple of reasons, normally the boss hens are the first to breed so it makes sense to sound like one. By slowing the cadence you can sound like another gobbler or jake, and sometimes depending on the staging of the breeding cycle, they seem to prefer the company of other gobblers. As the breeding season progresses the flock begins to break up as the boss hens start to nest, the younger hens become receptive and the gobblers seem to be more responsive to a younger hen sound, as Silvestris noted soft clear yelps with clucks and purrs. This can also be a more natural sound as they become wary of not only hunters, they don't want to mess with the boss hen.
Hunting pressure can be a major factor especially if the gobblers have seen their buddies get smoked or have had a narrow escape themselves. As John mentioned they can become quite shut mouthed and wary after associating turkey calls (and poor calling) with hunters. The ones that won't answer are probably the hardest ones to kill, and I can think of a few around here that are like that. Last spring early season we found using fall calling tactics worked best for us,jake yelps, gobbler clucks on a tube call etc as they weren't responding well to any hen yelping I think due to the weather, humidity, stage of the breeding cycle. But then it seemed to change as the season progressed. I pretty much carry a box or two, couple of friction calls, tube, wing bone and trumpet, like Jeff says you never know what will trigger a response from day to day or area to area and I like finding birds that want to play.
Take my thoughts for what they're worth, every time I get too full of myself and think I'm a seasoned veteran turkey hunter, the turkeys find a way to humble me