In Super Mario Maker, with all the extra changes and removed elements, is it possible to create a level that is exactly like an original level in Super Mario Bros 1, 3, Super Mario World or Super Mario Bros Wii? I can accept not having the exact same backgrounds, as that would not affect game play.
I would say that for some worlds, yes it's possible.
Take world 1-4 from the first Super Mario Bros game. Here is a video of a near exact replica (with a few differences in textures and the floating bridge above Bowser at the end is longer than the originals) with the level ID in the description. For comparison, here is a video of the original game.
There is also a Reddit for worlds 1-1 and 1-2. They provide the level ID's, but whether or not they are exact I'm not sure since I can't play them. It's mentioned that they are as close as possible to the originals with the exception of the limitations imposed in Super Mario Maker.
There's one important thing in Mario Maker that you have to pay attention to if recreating a level from Mario 1, 3, or World. The physics engine used in Mario Maker is the same one used in New Super Mario Bros, which is different from those used in the original 1, 3, and world. And it uses the same physics engine no matter which types of game theme you choose.
This means that it could be possible to recreate a level that is 100% identical to a Super Mario World level in terms of the layout of each individual block, enemy, etc; but the level would play differently; and could even be impossible to beat in Super Mario Maker.
For example, in original Super Mario World, when you spin jump on an enemy and it dies, you don't bounce off of it at all; you go straight down. But in Super Mario Maker, spin jumping on an enemy to kill it causes you to bounce off it like you do with a normal jump. The basic mechanics of the angles and speeds of jumps differ as well.
That being said, the other answers are correct; you can recreate some levels, but not others; due to various types of enemies and blocks not existing in Mario Maker.
First, do you mean the ENTIRE game? If so, I don't think so. Some levels have multiple exit pipes that lead to areas with different sprites and the sub-area would take up the entire length of the level anyways. So for the whole game, no. (But I would love to see an attempt). If you only mean one level, it depends on which level you select. For example, in Super Mario World, there are blocks that expand and compact up (like the ones in YI 3). Those (as far as I know) are not available in SMM. So, long story short, it depends on which level you pick to duplicate.