AKA 'gaff tape' or 'gaffers tape'.
It's used especially during filmmaking and theatre production for a variety of things. But it's a good general-purpose tape that more people should use.
Reason for existence — Gaffer tape's main goal is to minimize residue after removal. Gaffer tape might be in place for hours, days, or even months. There's always a chance that a little residue will be left, especially if it was in place for months, but usually there's so little residue that it's easy to remove manually, and gaffer tape beats all other tape by far at this.
Its second goal is to adhere as much as possible, given the constraints of the first goal. (It's almost like a much stickier version of painter's tape) And it's pretty durable too.
Downsides — Gaffer tape is expensive. And you have to get the good stuff — there are many off-brands available, but they're mostly a complete waste of money. Plan on spending ~$20 per roll.