MAME does most of the 8-bit and 16-bit consoles to varying degrees of accuracy, in many cases perfectly acceptable. That is, if you're actually using MAME (not some hacked up clone build) and actually using something semi-recent (newer than May 2015)
It's actually kinda funny reading through this thread, because yeah, while a lot of console games DON'T lend their control schemes well to an arcade, there are probably actually more good console games that do than good arcade games, simply due to the sheer number available.
Obviously the key thing is genre. Fighters, puzzle games, shmups, platformers etc. are for the most part going to play just fine, likewise games released for systems like the A2600 which had a similar level of dumb simplicity to their gameplay meaning they work as pick-up and play arcade style games.
There are even plenty of games for the 8-bit home computers that are fine if you automate the loading, the only times you have to be careful with them is high scores etc. as many expect you to enter initials with a keyboard, which obviously doesn't map well, but still, you can put together a good collection that don't; something like Manic Miner still plays just as well as an arcade game.
Even PSX era, there are games that didn't use the analog sticks (remember, the original model didn't even have them!) and don't even make use of the shoulder buttons.
Also, if you think about it, while nobody in their right mind is going to tell you it's a better game, something like the Genesis version of OutRun is actually more suited to a standard upright arcade cabinet with stick+buttons than the arcade version because the port was designed from the ground up for digital controls, whereas the arcade was meant to use a wheel, so unless you have one, won't play as it should.