I'm going to run a campaign and I was wondering if other GM would put this item into there campaigns.  

Yes, I have recently. In Dungeon of the Mad Mage, level 1! lol. They are now on level 2 and still have not chosen cards. I think they are afraid. Muahahaha.

 Once they choose, it will disappear and then reappear later on in the campaign.

No, I think its gimicky and disruptive.

I once added is a sort of a side quest to my campaign. Players found cards during their adventures which didn't do anything by themselves but if they managed to find the whole deck it would be glorious. Sadly that campaign ended before they managed to find the cards, I've wondered if I should start a new campaign where the main goal is to find the whole deck.

No.  While the DoMT is undoubtedly cool, I enjoy it when the PCs motivate the story rather than a random card.  Most of the picks are devastating to the Player and thus the story.

Quote from Houligan >>

No, I think its gimicky and disruptive.

 100% this.

I've already introduced this into a campaign, but with some good logic. The players know the cards are in it, I took out the game breaking super death cards, they don't know its a deck of many things though. It is a campaign where the continent is blessed with magic though, and they could research a magic item like this fairly easily, it also makes magic items like this not far fetched to put in.

I voted yes, but for me it really depends on my player base.  In my current campaign, I would most definitely do it as it consists of a bunch of middle schoolers who would be absolutely delighted by the sheer craziness of it.  I certainly wouldn't introduce it without having a good understanding of my players.

No.

Unless I have decided I could care less about the campaign, the characters and where it might go then I would never use it. It is highly disruptive, and the cards drawn can either completely remove characters from play or rewrite the direction of the campaign if the characters decide to try to deal with some of the negative situations that will result from the cards. You can also get characters becoming much more powerful than their companions in the group. All of these effects can effectively destroy an on going campaign. I've seen it happen at least three times. Twice as a player, once as a DM. I'd never toss it into a game I or any of the players cared about.

 P.S. That said, some great fun was had pulling the cards and seeing what happened to the characters ... the random chaos was cool ... the long term impacts on the campaigns were not. The campaigns were never the same afterward and did not last more than a session or two after the effects of the deck were implemented.

I would do it for a 1-shot.

There's always the somewhat toned-down Deck of Several Things from Lost Laboratory of Kwalish (or similar homebrewed variation) as a softer less permanent option.

I probably wouldn't add it for the obvious reasons, but if I did, I would add the condition that a character can only draw from a given deck one time.  They can still draw multiple cards as per the description, but once they've drawn their chosen amount, any additional cards will have no effect.

If you really want to use the deck, maybe just do a one-shot adventure focused around that. The thing can and will trash your game.

There should be a third option: "Yes", "No", and "Yes, but only under certain preconditions".

I wouldn't be against throwing them in, but....

1. They would not be an obvious find. They would be in a large lootable area, and only a certain high investigation check would find them. 

2. Only after the party has reached at least 10th level, because by that point the epicly dangerous game-changing effects of the cards are fairly within the realm of their own capabilities. 

3. I would probably customize the deck a bit, by changing some of the cards, partly to help guide the campaign along a certain path, and partly just because it'd be fun to create a custom Deck. 

Not only would I, I bought a deck off of Etsy that is pretty damn cool! They are only fun at higher levels when the consequences are real.

Who knew the deck was such a polarizing issue? lol.

To the OP, check out this video on ways to run the deck of many things. It's how I do it too. Matt has great insight on the infamous deck.

https://www.youtube.com/watch?v=b5pz46kEhIM

Depends on the players, the characters, and the campaign.

But did Critical role use it during there campaign?

Yes, but no.

In other words, it depends.