Note: I'm not distributing emulators! Google is your friend.
Umm, why not? Most emulators are free, contain no copyrighted code, and are completely legal. There's no trouble to be had for distributing them, or at least linking the best in each category.
Nintendo 64 : The first console that has 3D models in it (besides maybe 1 or 2 games on the SNES) and is really easy to emulate too. No problem here.
Except PC-FX, 3DO, Atari Jaguar, Playstation, and SEGA Saturn.
PlayStation One : Well-known but a bit sloppy to emulate on too old machines, there are still a few problems but it's still good.
Less demanding to emulate than N64. pSX requires a slightly faster machine, but still most anything you can find will run it just fine. ePSXe will work on damn near anything, though; its requirements are crazy low.
Nintendo DS : A bit harder to emulate, but not something difficult either.
Nintendo DS emulators have trouble with a lot of games, and some games won't even run at fullspeed with any processor not from the last year or so. DS emulation is not very sophisticated at all.
PlayStation Two : Now it gets interesting... An emulator DOES exist, however it can be slow on most machines even if less than a year old.
It really depends on the game. Some games run at fullspeed on almost anything, and some on almost nothing.
Game Cube/Wii : Two good consoles with a good emulator but can be slow, depending on your machine.
And also depending on the game, and your settings. Although interestingly, Super Smash Bros Brawl will run great on less recent machines, but games you'd expect to be less demanding such as Sonic 4 struggle even on good ones.
But more than anything else, I question why this thread was necessary. We don't frequently get people asking for a PS3 emulator so they can play the FF7 tech demo, or any stupid crap like that.