Slayer

Has nothing to do with the anime Slayers.

Slayer is a title that gets bandied about a lot on /tg/, but the two most prominent /tg/ references are as follows.

Warhammer

In Warhammer Fantasy, dwarves who feel too ashamed to live with themselves take up a ceremonial pledge to the god Grimnir. They tattoo themselves, dye their hair red and spike it into a huge mohawk, grab the biggest weapons they can, and set off to redeem themselves through dying in battle. Of course, they can't just kill themselves; they have to fight as hard as they can and to the very best of their abilities, until they fall against a nasty legitimately too mighty for them to overcome. Sort of like a super-metal paladin, or a non-weeaboo dishonored samurai.

The most famous Slayer is the titular star of Gotrek & Felix.

In Warhammer Fantasy Roleplay, Slayer is a career path that dwarves can enter, but it is a one-way trip; other than the more powerful levels of Slayer, they cannot ever change out of that career. It's a brutal combat machine, but utterly useless at anything else.

Pathfinder

In Pathfinder, the Advanced Class Guide splatbook introduced a bunch of new classes, which basically ripped off the idea behind 4th Edition Dungeons and Dragons's Hybrid Classes: each class was basically a fusion of two existing classes. The Slayer is a Rogue/Ranger hybrid, essentially what happens when you take the the combat abilities of the rogue and ranger, but ignore the rest of their abilities.

They are good at tracking and stealth. They have a weaker version of favored enemy that they can apply to any one target at a time as a move action(swift at level 7). They get sneak attack dice every third level instead of every odd level, and have D10 HP, great BAB and good Fortitude and Reflex saves. At level 10 though slayer becomes the king of stealth takedowns when he gets access to the "Assasination" talent, allowing him to insta kill an unsuspecting enemy with a single sneak attack(if the enemy fails a pretty high fort save that is). This talent is not limited by "per-day uses" and can be used on any studied target that hasn't spotted you or recognises you as a foe. The save also scales with your level and Int modifier, so unless your enemies have death attack immunity they won't make it out alive most of the time. If the target survives by making the save, spots you on time or you don't attack within the time alloted after you studied the target you will not by able to use the talent on the same target for the next 24 hours. So plan carefully.

Great if you really, really want to play a Bounty Hunter type character, as that's basically what they were designed for; people who thought the Rogue was too squishy and the Ranger had too much wanna-be spellcaster baggage.