Why does a "typical" hydrogen atom have no neutron? There are quite a few sources (mostly high-school physics textbooks) that I've read which don't give the disclaimer that the hydrogen atom they are using in a diagram is an isotope (as in having unequal neutron and proton count).
Why does the "typical" (in quotes due to a lack of a more scientific or precise term) hydrogen atom have 1 electron, 1 proton, but no neutron?
What's the reason?
 A: The most common isotope of hydrogen has no neutrons.
Other isotopes are deuterium with 1 neutron and tritium, with 2 neutrons.
Since virtually all (99.98% according to wiki) naturally occurring hydrogen comes in the no neutron isotope, it seems reasonable that books show a schematic of that one when illustrating hydrogen.
As a secondary motivation, the one electron + one proton is the simplest atom you can imagine, thus it makes a good choice.
In terms of lexicon: every atom is an isotope of a certain element. Also, every element comes in different isotopes, which differ only by their number of neutrons. I presented to you three isotopes for the element hydrogen. In this case, there is an overwhelmingly "standard" case, in terms of abundance, so we feel safe calling one particular isotope with the element's name. In other cases, this choice will not so self-evident.
A: It's possible to imagine living in a different universe where most nuclei of the element with charge 1 were deuterium, and the lighter protium was the rare outlier.
However, we don't live in that universe.  Most of the ordinary matter in the universe is hydrogen (75% by mass) and helium (25% by mass) which has been unprocessed since the Big Bang.  Deuterium is an especially fragile nucleus: it has no excited states, but fissions into a proton and neutron when hit by a photon with energy higher than 2 MeV.  Once this fission occurs the neutron has only about fifteen minutes before it decays into a proton, electron, and antineutrino.  
So even if there had been a period early in the history of the Universe when most of the matter was deuterium, the deuterium would have dissociated into free protons and neutrons unless the temperature were already below 2 MeV.
(I'm not even considering tritium, which has a half-life of about 12 years.)
A: The chemical properties of an element are always determined by the atomic number, that is, the number of protons in the nucleus.  All carbon atoms have six protons, all iron atoms have 26, etc.  It's the atomic number which is featured prominently in the periodic table, for example.
Until the neutron was discovered in 1932, this was fine.  After the neutron was found to occupy the atomic nucleus along with protons, then another name had to be coined for atoms having the same number of protons but different numbers of neutrons in the nucleus.  This term was "isotope", which means "in the same place" (on the periodic table, i.e. having the same atomic number.
Some isotopes have fewer neutrons than protons, some have the same number of protons and neutrons, and some isotopes have more neutrons than protons, but as long as a collection of atoms all have the same number of protons, then all the atoms in that sample consist of different isotopes of the same element.
In all cases, the number of protons + the number of neutrons = atomic mass number of an atom.  Carbon-14, for example, contains 6 protons + 8 neutrons to make the atomic mass number of 14.  U-238 has 92 protons and 146 neutrons, while U-235 has 92 protons and 143 neutrons.  Chemically, both uranium isotopes behave identically, but U-235 can sustain a fission chain reaction while U-238 cannot.  Those three extra neutrons make a difference on the atomic scale.
