Question: I am just wondering, does anyone have all the badges on Stack Overflow?

Answer: 
No, no one has all badges on Stack Overflow.

It is not possible.

For example - the [Precognitive](https://stackoverflow.com/help/badges/892/precognitive) badge cannot be awarded, as the site existed before the Area51 process came to being.

This of course excludes all tag badges, which would require someone to have score of 1000 in each and every tag...
Assuming the question is referring to only the top level badges that aren't for specific technologies, [this SEDE query](https://data.stackexchange.com/stackoverflow/query/1354513) lists the StackOverflow users with the most distinct badges.

At the time of writing there are two joint top users, who each have 84 out of a possible 91 badges. However, it's worth noting that some of the badges have now been retired (see [bottom of this page](https://stackoverflow.com/help/badges)) and so are permanently unattainable for users who do not already have them.