I came across this video on youtube on how to get all three starter pokemon on pokemon gold and silver. I haven't tried it on pokemon crystal but it may work on it also. Any way i hope you enjoy the video as much as i did.

https://www.youtube.com/watch?v=XUEMJr2vXhk

Sorry but it is not possible to get the 3 starter Pokémon you can only choose one Cyndaquil Totodile or Chikorita you can trade to get the others

Yes it is possible. I did it myself, i posted a snap shot of all three of them on here. Watch the video and give it a try. It took me about 5 minutes 2 do. Here is what you do. Before you talk with professor elm save your game in front of the three poke balls. Talk with elm and pick what ever pokemon you want. Go through the story until you get your poke balls from his assistant. Give one of your poke balls 2 your starter pokemon and catch a wild pokemon. Deposit your starter pokemon into the box and do the box clone glitch so you will have one in your box and one of them in your pokemon list menu. Next load your game so your in front of the 3 pokemon and pick a different starter pokemon but this time don't save your game. All you have 2 do this time is go 2 a pokemon center and withdraw your starter pokemon that you picked the first time and take the ball you gave 2 it. Catch another pokemon so you can put your first 2 starters in your box. Do the clone glitch again and this time pick the third starter pokemon. You will have the first two pokemon in your box. That is how you get them all. Watching the video will explain it better. 

Also don't save your game UNTIL you get all 3 or you will mess the glitch up. 

The first two pokemon won't show up in your pokedex but when they evolve the evolved forms will show up. Only your last pick will show all 3 of them in your pokedex.

CPartydog : Yes it is possible though it requires a really complicated glitch at least for me it does :3

Wow  really well this new for me  every day learn something new thanks for the info well lets try

Your welcome. I don't see how the glitch is hard 2 do. All you do for the box clone glitch is save your game in front of the computer in the pokemon center and put your pokemon in the box and change 2 a new box, when it is says don't save the game just close the window and start the game back up and when you start the game you will have one of the pokemon in your pokemon list and one in the box. But when you are doing this glitch don't save in front of the computer or you will mess the glitch up. You have to be in front of the pokeballs before you talk with elm or the glitch wont work and you will have 2 start all over.

bloodyb : Yeah but most of the time my save corrupts and I have to repeat everything again that is what is hard it's all the timing.

Just time it like this. As soon as you see saving. Close the game.  The easiest way 2 do it is just have your mouse over the x on your page window before you start the glitch. 

Ahh... that good old glitch. I use that all the time when I start up a new Gold or Silver game, simply because I don't have a trading cable and I want all three starters for the pokedex.
I use it for more than just starters though. I also use it to clone Eevees and trade pokemon, and it even works with items (Just equip the item you want duplicated onto a pokemon).
You can also use this for the first gen games, though your game file is much more likely to corrupt than in Gold and Silver.

Gamin'Gal :

Yep it is the easiest way 2 get a ton of master balls. The cloning of eevee really is the most useful if you want both espeon and umbreon, since eevee evolves with happiness it literally cuts the time in half. 
In first gen games it is pretty impossible 2 clone with the boxes. Their is no way possible 2 time when 2 shut off when you save the game. About the only thing that will work is the trading with the game link cable clone glitch. You can't do that on here for obvious reasons.

bloodyb :

Gamin'Gal :
I've heard it being done with the box before as well but i personally don't think it will work and the people that say it can are just bs people. When you change the boxes it saves in about 5 seconds and it don't tell you when it is saving. Doing the box glitch works with timing and knowing when 2 turn off, which on second gen you can see the message, unlike with first gen games. I just don't see how it is possible with first gen games. The game link cable cloning does work with first gen. I use 2 use the game link cable glitch when i was a kid. The box cloning is not something that i personally think will work.  Also on second gen you have 2 give your pokemon a ball and on first gen you can't give any items 2 your pokemon.