Ive found everyone plays the game differently, among other games.

How do you play SMB (Nes)?

I like to run through the entire game, as fast as possible, never letting go of the run button.
seeing how long i can go without taking damage.

Ive successfully gone through both runs (normal and hard mode) of the game without taking any damage.
This is on the official hardware, with no cheats.

My runs in terms of speed aren't record breaking however, i generally screw up on 4-4 and 7-4 when missing a jump, or jumping too soon.

I don't usually play the game with any rhyme or reason. However, I typically skip the warp zones, and usually I try to collect any and all coins located in plain sight. It's rare that I visit any of the coin rooms, other than the one in World 3-1.

I'm actually (terrible secret) not very skilled at platforming, despite playing a lot of them, so I tend to take everying kind of cautiously.

Also, for this game in particular, I jump over or avoid enemies instead of killing them most of the time.

I play all different ways. Sometimes I fly through the levels as fast as possible. Usually I try to collect everything and break as many bricks as possible. I like jumping backwards sometimes, I know it has no real effect, but I think it looks cool to time your jumps and then turn at the last second to jump backwards.

I'm more of a running before thinking when I play SMB. Unless it so happens that the stages requires me to think.

I tend to just take my time on levels where it is possible to do so. I can run like crazy on just a few of the courses but I forget which. Rather poor reaction times have been plaguing me for some reason.

This might sound weird, but I've personally never played the game.

aww,
you should some time, its a classic,

if you have a wii, they did port the SNES version of mario all stars, which has SMB1, smb2j, smb2USA, and SMB3 on it.

You could rent it,

I have SMB3, if that counts.
I'm sometimes a strategist, trying to get all the secrets, but sometimes I run through the stage as quick as possible.

smb3 counts