With the amount of games in the series, there's bound to be some ideas that don't make the cut. This can range from unused textures or animations to entire characters and story elements ending up scrapped. This is by no means an extensive list of cut content, just some especially infamous examples as well as things i found interesting. If you want to learn more about unused content from Metal Gear games (and a bunch of other games), i'd highly reccomend going to The Cutting Room Floor.

Starting off with a fairly well-known one, Kojima originally wanted The End's boss battle in Metal Gear Solid 3 to last several real-life weeks to make for a more realistic battle, with the player having to slowly take advantage and take down the legendary sniper. However after some tests the development team were told that it was impossible and not reccomended.
Source

I found this video recently, it shows off unused animations for MGS1. The thing that stood out the most to me is that there's a crouch walking mechanic, which wasn't fully implemented until 4.

In Metal Gear 2: Solid Snake, there's an unused radio call from Campbells frequency. The dialogue, when translated to english, is as follows:
"Mister, are you Snake?
It's me, Carrie.
Daddy went fishing.
But it's alright...
He took the codec with him.
The number is 140.99.
Come and play with me next time. Bye."
This call obviously isn't from Campbell, but from Master Miller's daughter Carrie. She is also mentioned in the game manual. I think this call is really cute, it gives the characters more depth and I'm not sure why it wasn't included.