Is there any hard evidence that rogue planets exist?

Giant planets when first formed are big and hot. They radiate their own light, mostly in the infrared. So young isolated planets can be seen directly.

There have been various claims in the literature that objects as small as a few Jupiter masses have been identified in young star forming regions. See various papers by the IAC brown dwarf research group

http://adsabs.harvard.edu/abs/2000Sci...290..103Z

http://adsabs.harvard.edu/abs/2002ApJ...578..536Z

http://adsabs.harvard.edu/abs/2014A%26A...568A..77Z

http://adsabs.harvard.edu/abs/2013MmSAI..84..926Z

Another object that is part of the beta Pic moving group, recently discovered by Liu et al. (2013), has an estimated mass of about 8 Jupiter masses (Biller et al. 2015).

http://arxiv.org/abs/1510.07625

These claims are open to criticism - sometimes it is hard to tell whether a faint object really belongs to the star forming region observed, rather than being an unassociated background object. The claimed masses also depend heavily on models for the luminosity-mass relation as a function of age, and the ages of these objects are not easily constrained. The likelihood is that at least some of these objects are below 10 Jupiter masses and would rank as planets by some definitions; though none of the individual objects could be said to be proven beyond any doubt.

Nevertheless it would not be surprising if, in the maelstrom of the formation of a cluster of stars, some planetary systems were stripped from their parent stars by close encounters with other objects and indeed numerical simulations of planetary systems in dense star clusters show that this process occurs (e.g. Davies 2011).

http://adsabs.harvard.edu/abs/2011IAUS..276..304DD

The chances of seeing older, isolated, planetary mass objects are slim, but microlensing appears to be the only technique presently available. The microlensing signature of a free-floating planet is of course unrepeatable so a discovered planet could not be followed up in any way. However, surveys of microlensing events could be a way of saying something statistically about how common such objects are. See for example http://astrobites.org/2011/05/24/free-floating-planets-might-outnumber-stars/

It is also worth noting that the whether these things really are "planets" at all is disputed. They could either be genuine planets, formed in the same way that is hypothesised for most giant planets - that is by accretion onto a rocky core that formed around a star. They could then have been displaced from their parent star by dynamical interactions with other bodies in their system or with a third body. As I said above, N-body simulations do predict that this will happen (e.g. Liu et al. 2013).

On the other hand they could represent the very lowest mass gas fragments that are able to form during the collapse and fragmentation of a molecular cloud and that for some reason were unable to accrete further gas (i.e. they are really more like low-mass brown dwarfs). This so-called "fragmentation limit" is of order 10 Jupiter masses, but if it were a little lower it might explain the free-floating "planets" that have been seen so far.