Is there any stable hadron? Neutron can decay into proton and I think some hypothesis claim that proton can also undergoes decay into subatomic particles... Is there any hadron that never decays?
 A: The question of hadron decay is intimately connected to the reactions of quarks, because hadrons are made of quarks. Weak interactions can transform the different types of quarks into each other, for example a neutron decays into a proton when a down quark decays into an up quark (and a W boson).
The up quark is the lightest quark so it can't spontaneously decay into any other quark. That means the proton can't decay into anything else via weak interactions. (You might think it could decay to a baryon with three up quarks, but the exclusion principle means that baryon has to have a higher spin and this means a higher energy. The baryon with three up quarks, the Delta, actually decays into a proton.)
In the Standard Model quarks can't just disappear so a proton is stable. Well, a quark and antiquark can annihilate and disappear, which is how mesons decay, but if we consider a single quark it can't just disappear. However theories have been suggested in which quarks can decay into non-quarks. As far as I know the earliest of these was the Georgi-Glashow model. In this model two up quarks can decay into an X boson, and this subsequently decays into a positron and an anti-down quark. This means a proton could decay into a positron and a neutral pion - the pion then decays into two photons.

But the Georgi-Glashow model has been ruled out by experimental measurements as it predicts too short a proton lifetime. Other more complicated models remain just viable, though the current lower limit on the proton lifetime is pushing even those models. As of right now there is absolutely no evidence that protons can decay. So until evidence to the contrary exists I think it seems reasonable to maintain the position that a stable hadron does exist, and that hadron is the proton.
A: 
Is there any hadron that never decays

The current experimental limit for the decay of the proton is $5.9\times 10^{33}$ years, so it depends what "never" means. The Avogadro number, number of molecules in a mole, is $~10^{23}.$ One would have to wait $10^{10}$ years to be at the experimental limit for a mole of matter. The experiments check for the decay of protons in enormous in mass detectors, and have not seen any, that is what the limit means.
So with "never" defined as "more than $10^{33}$ years of waiting for it to decay, protons are stable.
After all it was the assumed stability of the protons that built up  the conservation of baryon number and the isospin model for nuclear physics. Quarks, discovered later, were assigned 1/3 baryon number and can decay through the weak interaction to a lowest level, but still a quark will exist in the end of the decay chain to carry the baryon number. Unless the Standard model is superceded  aside by new data and new symmetries that allow for non conservation of baryon number, the proton can be considered stable. 
There exist rumours about leptoquarks at the LHC,  the X in John' answer. If they exist , then the proton can decay and there will be no stable hadron. Eventually, the weak interaction would get all the quarks, but the lifetime of the universe should be practically infinite. 
