It really depends upon how you define things, as the other answers have noted, perpetual motion machines violate the laws of thermodynamics, specifically the first and sometimes the second. However, if we remove systems that extract more energy from a system than is put in, we are still left with systems that are able to extract energy to produce useful work.
If we define unlimited free energy as a device that is able to run without human energy being put in (e.g. generated electricity, mechanical motion, etc.) then there are some devices that are able to operate on their own without an obvious means of input.
Clocks, such as the Jaeger Le Coultre Atmos is arguably one of the better examples of this in that it has no visible means of winding or putting energy into the system; however, it is not a perpetually motion device as it will eventually run down to to mechanical wear and tear due to the effects of friction.
However, this does raise an interesting point, while true "free energy" may not be possible, does energy extracted from existing system and used to perform useful work count as free energy? While it is obvious that there is a significant amount of energy put into the construction of the clock (or extract of wind, tidal, solar, water, etc.) the long term work produced like exceeds what humans have put into the system. This could also apply to the other forms of power generation cited which generate significantly more useful work for the amount of human work put into the system when compared to more primitive devices such as hand powered cranks.
Across the board though, the "unlimited" part of the equation is an issue as friction eventually wears things down if they are left to their own devices. Periodic maintenance can keep things running without too much effort in the scheme of things, but if that maintenance is neglected then the systems will eventually fail.
In summary, it is very unlikely we are ever going to have a means of getting something out of nothing; however, with proper application of engineering it is possible to extract more useful energy from a system than is put into extracting that energy. This arguably could be considered "low cost" or even "free" energy depending upon how much energy is invested in getting it out.