I love Splinter Cell.
The problem with stealth games is few of them actually exist as such. Over the last decade we've seen games like Splinter Cell which highly prioritized stealth move towards a more neutral position. In Splinter Cell 1, Pandora and Chaos Theory getting spotted was quite serious and possibly fatal, but with Double Agent, Conviction and Blacklist you could pretty much gun your way through most of the levels.
My recommendations would be:
Last of Us:
Last of Us tends to be more of a survival horror so stealth is inherently a mechanic that comes forward strongly throughout the whole game. Various levels also psychologically intimidate you into going silent rather than guns blazing through a very frightening ambience and setting.
While stealth mainly constitutes sneaking around in the first few games the last few games allow you to knock people out rather than brutally executing them. Blood Money specifically discourages killing everyone if you aspire to become a silent assassin so stealth can become a necessity.
Dishonored is arguably a classic stealth game. You don't have a machine gun or a warhammer to annihilate everyone once you're spotted. It's also interesting because the amount of people you kill influences the type of ending you get. So one could argue that the game is more morally aware than its assassin counterparts.
Deus Ex Human Revolution:
Deus Ex is one of those games where stealth becomes an option rather than a set approach. You can go guns blazing, but knocking people out while sneaking around can save you ammo for the boss fights and spare you some effort.
The thief games are proper stealth games. They're slightly more difficult than the rest I've mentioned and require you to be stealth in order to stay alive. I've played the 2004 and most recent one and I have to say, they're both brilliant in their own right. The 2004 one is a bit outdated and might not be as fun as it initially was, but the most recent one successfully revived the series. You can climb and scour the city while hiding on rooftops, ledges or sticking in the dark. There are various types of arrows at your disposal - from arrows that make a lot of noise (to distract the enemy) to water arrows that put out lights from a distance.
Metal Gear Solid series:
It's difficult to recommend a specific MGS game as all of them vary in difficulty and appeal. I quite enjoyed Metal Gear Solid 3 and 4. Up to Snake Eater stealth is paramount to your survival, but from Sons of Liberties onwards the game introduces you to an extended arsenal of firearms that allow you to fight your way out of almost any situation. The only problem with MGS is that its storyline is very hard to follow. I initially jumped in with MGS 4 on PS3, but soon found that I had no idea what the game was about. The cutscenes are also as long as 2 full films.
Assassins Creed series
I've pretty much played all the Assassins Creeds up to Black Flag. 1,2 and Black Flag were the best for me personally, but they all feature stealth.
I've only played Arkham City and Asylum for brief periods of time, but stealth seems to be an integrated part of both games.
Shadow of Mordor
The game based on Lord of the Rings has you playing as an assassin and feels like a mixture between Assassins Creed and Batman Arkham Asylum.
Death to Spies 1 &2
I never completed any of them, but they had interesting concepts. You're equipped with a sniper, sub-machine gun and pistol, but the missions have you acting more as a spy than assassin. It's pretty hard though.
Hope it's helpful