Concept Art

From the Metal Slug 10th Anniversary site (thanks to stoffhime1 for pointing this out to me). Bizarre fusions of the Metal Slug, including a UFO, the Ptolemaic armoured truck, the Slug Mobile with a drill on its roof, and a variety of ungainly mechs. The text is too small to make out, though it's likely early-days spitballing for vehicle ideas; it's dated a year and a half before the game's arcade release.

One unifying feature among the bosses' concept art is they're numbered differently than they are in-game, suggesting the level order was rearranged for the final product. Going by the art, the original order would be:
Mission 3 - Mission 4 - Mission 2 - Mission 1 - Mission 5

The scale saw some tweaking from tweaking from concept to sprite, and the front segment between the treads was changed to an elevator platform/hatch on the graphic. It's likely artistic license, but the art features the tank being operated by several soldiers, but there's no such indication in the actual fight.

This suggests the boss of Mission 2 would have approached you head-on as well, deploying small jets from between the cockpits. This port is still visible on the sprite when it's seen flying in the background, but it's never used in battle.

The small guns on the bottom are absent on the final sprite, and the turrets do not appear to rotate in the concept art. The hatch on the lower half looks to have been meant for deploying troops, but is used for the floor-destroying shockwave in-game; reinforcements just stroll in from off-screen.

Top: Early design. Below: Final design & sprite.
The original concept has barely any visual elements carried over to the sprite! The shape is more squat, the treads are different, and it boasts a wider range of armaments, including a second cannon on the back and a multitude of missile types, including cluster bombs.
The final design is much closer to the sprite, with only minor differences like the differently shaped entry hatch and repositioning the exhaust.

Concept art for how the stone turtle would have looked: apparently a reference to the World-bearing Turtle, it would have carried the elephant bosses and a three-storied tower on its shell, with the old man's pillar and his spinning tablets at the top. I can only assume the turtle's "stomach laser" would've warped the player straight to the elephant boss, or possibly inside its shell where the mechanical tower would've been? I hate to speculate.
Curiously, there are four elephants on the turtle's back, and the turtle has an extra head on its rear end.

An early renditions of the Ptolemaic mech with a far chunkier and mech-ier design, as well as an unused flight variant. Evolutions of these designs appear as sprites in the flyer below.

The game does a good job recreating the concept art, losing only some detail off the sides of the screen, the goofing-off soldiers in the far distance, and the podium with an officer pointing at the mugshots. This concept drops the line-up of mugshots, instead showing one character at a time for each player. Why mess with success?

The Slug Mobile's turret is the old side-view style (see unused sprites), except the turret is actually on the car and invading the space of the back window.

A promotional flyer for the game, but featuring sprites that don't appear in the game.
From the top, there's the boss of Mission 4 in a design very close to its concept art.
Between Eri and Tarma are the mecha units with very different faces and one sporting a small chain gun. Below Tarma is a totally unused jet hybrid mecha.
Below the unused jet robot is the boss of Mission 2; it's close to final, but missing its pilots and some of the detail around its edges. Compare!
And lastly, the bottom row features a tank with a giant radar dish as its cannon, also totally unseen in the final game.

Another flyer. Up above is the boss of Mission 2 (thanks to Ben Chan for pointing that out to me because I'm dumb), deploying two smaller planes just like in its concept art! Those jets are seen nowhere else in the game.
Over to the right is the Slug Mobile, which is occupied by an interesting pair. On the left is "Glen Achilles", while on the right is an unknown guy. He looks like the characters in their fat status affect, holding a fatty's bomb, wearing sunglasses and a Rebel soldier's helmet. It also looks like he has a white shirt, judging from his arm. Who is he? A scrapped helper character, like Glen and Hyakutaro? A character who was to appear in a movie scene? Very mysterious.

Ignition Entertainment's old MS5 site has a slightly larger image of the car and it's occupants just below it's menu.
Doesn't help us identify the guy, though. Some people say he looks like a portly Mr. Big from the Art of Fighting games. I say they're nuts.

Concept art is sourced from the Metal Slug 6 Art Gallery, the Metal Slug 10th Anniversary website and the Metal Slug Attack Illustration Gallery.