A lot of people think the franchise started on the PlayStation One. This was true for the Solid part of the series, but MGS has existed long before this. The original game was released back in 1987. In the years since then the series has evolved into one of the most prolific stealth video games on the market.
The story has evolved from being a basic “get in their and destroy the bad guys” to an incredibly complex story that intertwines through many characters across several decades. As a franchise alone, the MGS series is one of the largest and most well known video game franchises.
Now that Kojima is forever done making Metal Gear Games, any future entries in the series are not going to be as good. What are some other games out there that have attempted to copy the format? Even if there are no clones, are there any other good games like Metal Gear Solid?
Assassin's Creed: Origins

Kojima was a big fan of the Assassin's Creed games when they first came out. The stealth aspects of the game do have a lot in common with the MGS games. It is not as hardcore stealth and the setting is in historic times, so there are no guns, but the AC games are definitely good ones to check out if you want a game like Metal Gear Solid
Deus Ex: Human Revolution
Hitman: Absolution

Games in the Hitman series, particularly the newer ones are a lot like Metal Gear Solid. Very strong focus on staying undetected, but if you do raise the alarm, you can just start shooting the shit out of everyone. Fairly high production values too. I didnt find the story to be as interesting as the MGS story, but it's still a good game that is worth playing.