I like to engage in old school hex crawls from time to time (because I find fun and value in it), but I would say, mostly I use hexes to measure distance rather than to crawl. And I take a light hand with hexes (though it does depend on the setting and genre). Presently I run mostly wuxia campaigns. Also most of my campaigns take place in areas that are civilized, maybe with a frontier, but a known frontier. So mostly the players are doing things like saying they want to go north to the City of Dee (and they tell me what path they are planning based on their knowledge of the map). Then generally each Hex (depends on the scale) would be a Survival Check to see if anything happens. And I would use random encounters (but those tend to be keyed to local elements (for instance if there is a sect that operates in that area, they would be on the table-----and sometimes I have an entry on a table like 'pick something in that hex'). But these kinds of games are often more about the people and organizations living in the setting, than about clearing out hexes. But these wuxia campaigns are often blends of many things (there are dungeons in them, but also sect wars, grudges-----these are a huge part of my encounter table set up---romance, etc). I think some people see the maps to my settings and assume the setting is arranged like Isle of Dread (because of the hexes and the way terrain is rendered). But the drama and sandbox thing is pretty seriously baked into the setting material.
If you really want a sense of how I run this stuff, you can download Wandering Heroes of Ogre Gate for free at Drive thru, and just read the GM section. It is a bit out of date (five years old at this point, and I've certainly refined some of my thoughts, but it gets a lot of what I talk about here----and in a less extreme way because I am not contrasting against an alternative style of play in the book----which is one of my frustrations when I engage in these threads (I find myself staking positions and losing sight of actual play).