Metal Slug X had nearly all of Metal Slug 3 in it, except for the last level. Evidently they had the game half done by that point but decided to remix Metal Slug 2 first (rightly so because MS2 had so much slowdown, it was unplayable).
Metal Slug 5 had many things in it that got cut, the game was probably rushed. In the final level you had to fight the cultist leader, a gigantic stone turtle, and there was a special prisoner who was a commando similar to you, once freed he follows you and shoots enemies not unlike Hyakutaro. The last scene of the game makes significantly more sense with the missing bosses put in place and it was also an allusion to Atuin (the stone turtle, carrying the elephant robots, on which the final boss area resides).
There's a fan patch that restores some of it, but who knows if it is done as intended. The concept art shows the area just like Atuin, but the fan patch has the stone turtle as a separate enemy before the elephant pillars.
Streets of Rage 3 had auto scrolling bike levels, at some point you may have been able to pick up bikes in normal levels too, some cut moves, and a good third of Stage 6 cut out. On stage 6 you were meant to locate the general, then a path on the bottom would open up, connecting to the right side of the complex. You'd have to find the exit yourself.
And of course the western game was bastardized completely compared to the Japanese original.
DeCapAttack was also a western title that had everything in it changed, not unlike Puyo Puyo or Mario 2. The Japanese version was Magical Hat no Buttobi Turbo! Daibouken. They took the basic gameplay but changed the setting completely. For the better in this case.
You might want to browse TCRF.net, it's a site dedicated to cut content.