Is there any hard evidence that rogue planets exist? A rogue planet (or a rogue anything, for that matter: a celestial body other than a star) is something that's drifting through space without being attached by gravity to any star. They're just out there in the big black void. Is there any evidence that they actually exist? Or are they purely hypothetical?
Rogue planets have been discovered by infra-red imaging because planets are hot when they form.  Here's a list of a few.  

There's 2 types of Rogue planets.  One is failed stars.  condensing pockets of gas and dust that form similar to how our solar-system formed, but that are too small to form stars.   Source.

The 2nd type is planets that escape from a star's orbit.   This can happen by the star ejecting material and losing mass which causes the planets to expand in more distant orbits, some eventually escaping, or by gravitational assist either planet on planet or by two stars passing quite close to each other.    It's statistically impossible for Rogue Planets not to, from time to time, get ejected from solar systems, so they have to exist at least in reasonably large numbers throughout the galaxy, though I don't think it's well known how common there are.   

Our solar-system might have ejected a planet - see here.   In general, larger planets can eject smaller ones but mostly not the other way around, but two stars that pass too close to each other can eject any planets, mostly ones with more distant orbits.  A star that loses a lot of it's mass or a star that goes nova can push planets out of it's orbit too.