H+ is simplified writing. Here probably in water, where the proton is surrounded by water molecules properly oriented. Under usual conditions, this dissociation is very rare (but it determines many processes): you might evaluate how many moles of water fit in a litre, and compare with for instance 10-7 moles of H+ per litre.
Elsewhere, outside a solvent or a crystal, such dissociations in ions use to be negligible under usual conditions.
As for neutral hydrogen, H2 is the only observed form under usual conditions, but if hydrogen is hot, around 3000K it begins to split into atoms, and at 6000K (Sun's surface) diatomic molecules are scarce. Under big pressure, hydrogen makes a metal, hence one huge molecule.
All elements can dissociate to lone atoms with heat. Most gaseous metals comprise mainly lone atoms. Oxygen dissociates in the shockwave of space craft reentering the atmosphere. Nitrogen would dissociate at a higher temperature.
Many pure elements can make varied molecules. O2 can become O3 (ozone, unstable). Sulphur is known for allotropic changes, check Wiki. Carbon can make C, C2, C3 and more as a gas, diamond or graphite as a solid, C60, C70 or nanotubes mainly as a solid.