Chemical properties of isotopes
Short answer: nuclear neutrons greatly affect chemistry involving hydrogen.

Longer answer

Hydrogen is the lightest element, and deuterium is just less than twice as heavy. This makes a pretty massive (pun intended) difference to any vibrational modes involving moving hydrogen/deuterium. This means that, for example, the deuterated equivalents of weak acids are less acidic, and any reaction involving the loss of a proton will be significantly slower with the deuterated version.

Since helium is pretty unreactive, and by the time you're at lithium an extra neutron is only increasing the mass by about 14%, the effects on reaction energetics are much, much smaller for anything else.

I'd suggest looking up the "Kinetic Isotope Effect" for more information and more complex effects the mass change on substituting isotopes can cause to chemical activity.

As Eric Brown said in his answer, different isotopes may also have very different spectroscopic properties if the spectroscopic technique depends either on vibrational or nuclear properties.

As a minor curiosity, I'm given to understand this also means that heavy water is mildly hazardous to your health, since deuterated water and deuterated analogues of various vital chemicals have a nasty tendency to react mostly irreversibly or very slowly with vital enzymes that are "tuned" for hydrogen.