If you haven't seen the Anime/Manga Attack on Titan you are missing one of the better ones of this generation. It's horrific and yet damn perfect when dealing with fighting something many times your size and power. The 3D movement gear, the specialized weaknesses, the ease in which giants can murder people. It's blood, war, and all the nasty things that Hero vs Monster stories leave out.
But we know that right? Years of fighting Dragons, giants, and other monsters. Mind you, it depends on the system and just how casually you can die in it. The reason why I love Attack on Titan so much is the attention to detail about the combat. It's not your typical fantasy plot, it's not dungeon crawling, it's raw military tactics versus things that man was not meant to deal with.
I want to stress that Dungeon Crawling is a completely different story and skill set than full on Monster Hunting. The key difference is Monster Hunters (slayers), or whatever you call them, tend to be focused on more war like logistics. They tend to have a wider range of tactics and well 'killing' options. Take a look at Hunger: The Vigil or the various Monster Hunter games. The tactics are more focused on luring monsters into kill positions, traps, keeping civilians out of the way, and a lot of laying ambushes. By inverse behavior, dungeon crawlers AVOID ambushes, work their way through traps, and tend to pick up specialized weapons. A true monster hunter tends to use a lot of different weapons and tactics. Unless they fight just 1 monsters. But even then there will be a wide array of take down techniques. There might be some cross over, but a well done Monster Hunting game doesn't get into the 10 X 10 room mentality, I hope.
I have my own Monster Hunter variant game I call Griffin Guard. It's a team of convicts, petty nobles looking for status, foreigners, and general dregs of society thrown in a murderous 5 year 'service' where if you live the 5 years your past is wiped clean, you are given an honorary title of status, and let go with a small stipend. if you do MORE than 5 years with the Guard your status raises greatly, but people think you are CRAZY. The idea is a low magic fantasy world where monsters are a real problem and the PC's are sent into suicidal situations where wits and luck might keep them alive long enough to end their 'service' period. It would involve taking down all sorts of monsters, making gear to take down others, selling left over body parts, etc.
X-Com is technically a monster hunter experience in modern terms.
The best video game example recently besides Monster Hunter series could be Dragon's Dogma or God Eater. The idea is the same and it's fun and different break from the typical dungeon crawl. Not that it's better, but I'd LOVE to see a dedicated Fantasy Monster Hunter game with high attrition rate, maybe using the Only War style squad mate mechanics from 40K. Focused more on dealing with all sorts of monsters and having class specialties based around the way they fight. Highwire style Attack of Titan giant killing, undead disrupting via Holy writ, maybe cold iron and silver weapon specialization based on type. Monsters would have specific weaknesses and the PC's would exploit them to win the day. Hell, you could do it in FATE or a similar style game.
Then we make weapons out of their shin bones. If they have them.