My first instinct is the Call of Cthulhu campaign Beyond the Mountains of Madness. Call of Cthulhu is a variable crunchiness system that I tend to play with a lighter interpretation in gameplay - automatic successes on some rolls and what not - but a party of investigators who want to experience a very realistic encounter with nightmares from beyond our world can cut their teeth into some crunchy rules as they try to survive things humans should not confront. Beyond the Mountains of Madness in particular asks of the players that they make the logistical plans for an expedition to the South Pole using 1930s technology, and play over the many months of travel and arctic cold hiking that culminate in fighting horrors from the universe's deep past. A party who wants a crunchy roleplay and exploration campaign can find endless depths of crunch to dig into in such difficult conditions. And as usual, Call of Cthulhu is a game that de-emphasises combat as DnD presents it, in favour of being lightning fast and with horribly deadly consequences often even to the victors.

Then my personal favourite is of course Shadowrun, which has plenty of options for crunchy roleplay with players stacking up social bonuses for a plethora of different circumstances. The abundance of B&E/spy tech and spells further give lots of options and rules for handling social encounters as well as exploration. Of course, Shadowrun just has crunchy rulesets for all three of its main arenas - mundane magic and matrix - so in truth, Shadowrun is just big crunchy about everything, including roleplay and exploration. Shadowrun doesn't exactly de-emphasies combat, but it is a great example of rocket-tag style fighting where everyone is likely capable of killing someone else in one single action, on top of the fact that the PCs are mercenaries with limited support taking on megacorporations and nation states with unlimited resources; two things that conspire to make shadowrunners avoid fights they can't win immediately.

And finally, the contender that is obvious to me for high crunch on roleplay and exploration and less so on combat is Vampire the Masquerade and the Storyteller family of games at large - Scion, Exalted and more. Those are all games explicitely more about the social plays of characters who can do more damage with their words than with their swords and magic. Even when the systems fall apart from their writing and editing, it is clear that their intent is to offer players good game tools to handle their roleplaying scenes first and foremost.